This thesis is composed of two parts; the first part deals with observations of the molecular gas towards an unlensed, obscured quasar AMS12, and the second part investigates radio undetected, optically selected quasi-stellar objects (QSOs) to determine the nature of the radio flux density distributions of these objects. AMS12 is an unlensed, obscured, z = 2.767 quasar which we observed with the Plateau de Bure Interferometer to detect carbon monoxide rotational transitions and atomic carbon fine structure lines in the molecular gas. We present new detections of the CO(5-4), CO(7-6), [CI]( ³P₁- ³P₀) and [CI](³P₂− ³P₁) molecular and atomic line transitions in this thesis. AMS12 is the first unlensed, high redshift source to have both atomic carbon ([CI]) transitions detected. The highly excited molecular gas probed by CO(3-2), (5-4) and (7-6), is modelled with large velocity gradient models. The gas kinetic temperature TG, density n(H₂), and the characteristic size r₀, are determined using the dust temperature from the far-infrared spectral energy distribution which had the following best-fitting parameters log₁₀[LFIR/L☉] = 13.5, dust temperature TD = 88 K and emissivity index β=0.6, as a prior for the gas temperature. The best fitting parameters are TG = 89.6 K, n(H₂) = 10 3.9 cm⁻³ and r₀ = 0.8 kpc. The ratio of the [CI] lines gives a [CI] excitation temperature of 43 ± 10 K, indicating the [CI] and the high-excitation CO are not in thermal equilibrium. The [CI] excitation temperature is below that of the dust temperature and the gas kinetic temperature of the high excitation CO, perhaps because [CI] lies at a larger radius where there may also be a large reservoir of CO at a cooler temperature, which may be detectable through the CO(1-0). Using the [CI]( ³P₁− ³P₀) line we can estimate the strength of the CO(1-0) line and hence the gas mass. This suggests that a significant fraction (~30%) of the molecular gas is missed from the high-excitation line analysis, giving a gas mass higher than that inferred from the assumption that the high-excitation gas is a good tracer of the low-excitation gas. The stellar mass was estimated from the mid-/near-infrared spectral energy distribution to be M* ~ 3 × 10¹¹M☉. The Eddington limited black hole mass is found from the bolometric luminosity to be M• ≳ 1.5×10⁹M☉. These give a black hole - bulge mass ratio of M•/M* ≳ 0.005. This is in agreement with studies on the evolution of the M•/M* relationship at high redshifts, which find a departure from the local value ~ 0.002. In the second half of the thesis we investigate the possible existence of a lower envelope in the radio luminosity versus optical luminosity plane. We select a population of QSOs from the Sloan Digital Sky Survey photometric quasar catalogue from Richards et al. The QSOs are within a narrow redshift band 0.3 < zphot < 0.5 and cross-matched with the 1.4 GHz National Radio Astronomy Observatory Very Large Array Sky Survey. The radio images extracted from the positions of the optical QSOs are retained if the flux integrated over the beam size of the radio survey is less than 3σIrms ≤ 1.35 mJy. The radio-undectected QSO population is split into eight samples depending on their optical magnitudes and stacked to determine the mean flux in each sample. The stacked mean flux is detected in all but the faintest optical magnitude sample. The radio versus optical luminosity relation from the stacked samples hint at a lower envelope in the radio luminosity which may be interpreted as there being a minimum radio jet power for a given accretion rate. Stacking assumes the underlying distribution of the property being measured is fairly represented by the stacked result. We investigate the underlying distribution of the radio flux density from the QSOs taking the noise of the sample into account. We find the distribution of the QSO flux density is modelled by a power-law with a negative index in all eight optical magnitude samples. This implies the mean stacked result is not a good representation of the distribution of the flux density of the QSOs and that there is no lower envelope. This highlights the danger of interpreting results from stacking without verifying the distribution is characterised by the mean stacked value. We appear to recover the quasar optical luminosity function when we model the distribution of radio loudness parameters suggesting that, since we are essentially holding the radio flux density fixed, the radio loudness is a function of the optical luminosity. This suggest that the radio loudness is not a fundamental property of the QSO but rather the ratio of two independent properties, the radio and optical luminosities. We convert the radio loudness parameter to jet efficiencies and find a minimum jet efficiency of ηmin = 4 × 10⁻⁴. We find there is no sign of a minimum jet efficiency as far as our data’s sensitivity limit allows, so we expect η<ηmin. Hence we provide an observational constraint for theoretical models of jet production in the minimum jet efficiency.

The recent observational data in cosmology seem to indicate that the universe is currently expanding in an accelerated way. This unexpected conclusion can be explained assuming the presence of a non-vanishing yet extremely fine tuned cosmological constant, or invoking the existence of an exotic source of energy, dark energy, which is not observed in laboratory experiments yet seems to dominate the energy budget of the Universe. On the other hand, it may be that these observations are just signalling the fact that Einstein's General Relativity is not the correct description of gravity when we consider distances of the order of the present horizon of the universe. In order to study if the latter explanation is correct, we have to formulate new theories of the gravitational interaction, and see if they admit cosmological solutions which fit the observational data in a satisfactory way. Quite generally, modifying General Relativity introduces new degrees of freedom, which are responsible for the different large distance behaviour. On one hand, often these new degrees of freedom have negative kinetic energy, which implies that the theory is plagued by ghost instabilities. On the other hand, for a modified gravity theory to be phenomenologically viable it is necessary that the extra degrees of freedom are efficiently screened on terrestrial and astrophysical scales. One of the known mechanisms which can screen the extra degrees of freedom is the Vainshtein mechanism, which involves derivative self-interaction terms for these degrees of freedom. In this thesis, we consider two different models, the Cascading DGP and the dRGT massive gravity, which are candidates for viable models to modify gravity at very large distances. Regarding the Cascading DGP model, we consider the minimal (6D) set-up and we perform a perturbative analysis at first order of the behaviour of the gravitational field and of the branes position around background solutions where pure tension is localized on the 4D brane. We consider a specific realization of this set-up where the 5D brane can be considered thin with respect to the 4D one. We show that the thin limit of the 4D brane inside the (already thin) 5D brane is well defined, at least for the configurations that we consider, and confirm that the gravitational field on the 4D brane is finite for a general choice of the energymomentum tensor. We also confirm that there exists a critical tension which separates background configurations which possess a ghost among the perturbation modes, and background configurations which are ghost-free. We find a value for the critical tension which is different from the value which has been obtained in the literature; we comment on the difference between these two results, and perform a numeric calculation in a particular case where the exact solution is known to support the validity of our analysis. Regarding the dRGT massive gravity, we consider the static and spherically symmetric solutions of these theories, and we investigate the effectiveness of the Vainshtein screening mechanism. We focus on the branch of solutions in which the Vainshtein mechanism can occur, and we truncate the analysis to scales below the gravitational Compton wavelength, and consider the weak field limit for the gravitational potentials, while keeping all non-linearities of the mode which is involved in the screening. We determine analytically the number and properties of local solutions which exist asymptotically on large scales, and of local (inner) solutions which exist on small scales. Moreover, we analyze in detail in which cases the solutions match in an intermediate region. We show that asymptotically flat solutions connect only to inner configurations displaying the Vainshtein mechanism, while non asymptotically flat solutions can connect both with inner solutions which display the Vainshtein mechanism, or with solutions which display a self-shielding behaviour of the gravitational field. We show furthermore that there are some regions in the parameter space of the theory where global solutions do not exist, and characterize precisely in which regions the Vainshtein mechanism takes place.

In this thesis, we present a comparison of the evolution of the massive galaxies in the 7.8Gyr since redshift z=1 to the evolution predicted from galaxy formation models. Observing the most massive galaxies in the Universe at high redshift is challenging due to their red colours, owing to both their intrinsically red Spectral Energy Distributions (SEDs) and their redshift. In Chapter 1, We produce a method using catalogue-level data to produce matched aperture photometry for the SDSS and UKIDSS surveys in order to extend the wavelength coverage of a sample of galaxies in order to improve the precision with which models can be fitted to photometric data for these high redshift galaxies. Our matched photometry has consistent colours with those of the full processing of SDSS+UKIDSS images performed by the GAMA survey, and produces magnitudes within ∼0.1 magnitudes of the GAMA photometry for all galaxies. This is reduced to within 0.04 magnitudes when all blended sources are excluded. We compute stellar masses by fitting a Maraston et al. (2009) LRG model to both our derived photometry and that of the GAMA processing, and find that our photometry’s best fit stellar masses are within ∼0.2 dex of that which comes from the GAMA photometry, demonstrating that the method is consistent with that of a full processing, and that it is possible to quickly compute matched photometry for large area surveys of complimentary wavelength coverage. This is of vital importance for upcoming surveys e.g. DES, VISTA, EUCLID etc. Fitting Stellar Population Models to galaxy photometry is a widely used technique in order to convert from observables (colours, magnitudes) to physical properties (mass, absolute magnitude, age). In spite of their widespread use, the optical and Near Infrared (NIR) properties of stellar population models are still subject to debate. Two of the most commonly used models are those of (Maraston, 2005) (M05) and (Bruzual & Charlot, 2003) (BC03), which can differ greatly in the NIR due to the M05 models’ inclusion of the TP-AGB phase, which was neglected for BC03 models. We explore the ability of these models to reproduce measured optical+NIR properties of galaxies in Chapter 3. We produce matched optical+NIR photometry for the subsample of the galaxies surveyed by Zibetti et al. (2013) (Z13) which lie within the UKIDSS imaging area in an attempt to reproduce the findings of Z13, who conclude that their optical and NIR spectroscopy is better fit by models from Bruzual & Charlot (2003) than similar models from Maraston et al (2005). We compare the observed optical+NIR Spectral Energy Distributions (SEDs) to those of BC03 and M05 models, as well as the approximate Z13 NIR fluxes. Z13 found that M05 models fitted to the optical data and extrapolated into the NIR displayed excess flux in the NIR relative to the data, and BC03 models are better at reproducing the data. However, we show that our data is consistent with both sets of models, and on average brighter in the NIR than that of Z13. We also compare the strength of spectral features in the optical to rest frame optical and optical-NIR colours, and show that our set of Composite Stellar Population (CSP) models agree well with data, with a preference for the M05 models, showing the validity of using these models on massive galaxies. A measurement of the Stellar Mass Function (SMF) of galaxies is a powerful tool in detecting evolution of the galaxy population. With a statistically complete sample of a galaxy population down to a given stellar mass, it is possible to calculate a statistically complete SMF down to this mass. Comparison of the shape of this SMF to that of a similar sample over a different redshift interval allows the evolution of galaxies over this redshift interval to be calculated, in order to determine whether these galaxies are forming stars, merging or simply passively evolving. For this purpose, in 4 compute matched SDSS+UKIDSS photometry for the AA omega KIDSS SDSS (AUS) survey. This is a 145.416 deg² area survey of Luminous Red Galaxies (LRGs) from redshift z∼0.5 to z∼1 located within Stripe 82. We fit this photometry to a Maraston et al. (2009) Luminous Red Galaxy (LRG) template to give stellar masses, and scale masses according to the magnitude difference between the matched photometry and the SDSS model photometry in order to produce “total” stellar masses. We produce a volume-weighted SMF for the survey, and find that our SMF is consistent with the Maraston et al. (2013) SMF from the BOSS survey, meaning that the most massive galaxies in the universe are evolving passively from z=1 to the present day, which is a challenge to hierarchical models of galaxy formation. Comparison of observed SMFs to those produced by galaxy formation models is a method of testing the ability of the models to reproduce the evolution displayed by the real galaxy population. This is therefore a test of the physics included within the models, with the level of agreement between the simulation and the real galaxy SMF being indicative of whether the modelling has incorporated all the processes in action in the real universe. In order to test the ability of the state of the art semi analytical models of Henriques et al. (2013) (H13 hereafter), we compare SMFs of the simulated galaxies to those of the AUS and BOSS surveys in Chapter 5. The H13 galaxies were tailored via the application of both the AUS and BOSS colour and magnitude cuts, and SMFs calculated within lightcones of the same area as the surveys in order to compare equal volumes. Our findings extend the conclusions of Maraston et al. (2013), namely that the most massive galaxies in the simulations are not sufficiently massive to agree with the observed galaxy population at this redshift. By extending this analysis to redshift z∼1, we can confirm that the discrepancy is larger at higher redshift, with the difference between the most massive galaxies in the simulations and those observed being log(ΔM/M⊙) ≃0.2 at z≃0.6–0.7, whereas going beyond this to the range z≃0.7–1 the difference becomes log(ΔM/M⊙) ≃0.25, as can be seen in Figure 5.6, which demonstrates that the simulations are failing to either form, or assemble, the mass quickly enough to reproduce the observations. Instead, the simulations continue to assemble mass through to low redshift at a higher rate than is seen in the galaxy SMF. These discrepancies may indicate that the physics of the simulations is not fully accounting for the real processes in the Universe,and that we do not yet have a model capable of reproducing the galaxy population in the real universe. Clearly semi analytical galaxy simulations need to be modified in order to reproduce the observations, before being further challenged by upcoming spectroscopic surveys of galaxies at redshifts as high as z=2 eg. eBoss, DESI.

The properties of galaxies, such as the galaxy red fraction and galaxy stellar mass function, have been shown to depend upon their environment in the local Universe. Large scale photometric surveys such as the DES and in the future Euclid, will be vital to gain insight into the evolution of galaxy properties and the role of environment through cosmic time. Large samples come at the cost of redshift precision and this affects the measurement of galaxy environment. In this thesis an analysis pipeline is constructed to derive galaxy parameters including absolute magnitudes, stellar masses and galaxy environments. The analysis pipeline consists of well established components, such as HYPERZ, that performs SED fitting and components that I have developed and tested, including codes to compute galaxy environment. Five methods to compute galaxy environment are implemented, including three fixed aperture methods, based on spheres, cylinders and cones, the Nth nearest neighbour method and the adaptive Gaussian method. The codes are optimized and parallelized and are executed on Portsmouth’s high performance computer cluster. The codes are thoroughly tested using mock data. Further testing is conducted employing GAMA data, with an external collaborator. The pipeline is applied to two datasets and the results lead to two scientific papers: Etherington & Thomas (2015) and Etherington et al. (in DES collaboration review). The first study is based on a low redshift sample drawn from the SDSS. Spectroscopic and photometric redshifts and also simulated photometric redshifts with a range of uncertainties are employed to study the impact of photometric redshift uncertainty on measures of environment as a function of the aperture parameters. The photometric environments are found to have a smaller dynamic range compared to the spectroscopic measurements because uncertain redshifts scatter galaxies from dense environments into less dense environments. With the optimal aperture parameter values, even for large redshift uncertainties, ∼ 0.1, there is a Spearman Rank Correlation Coefficient of ∼ 0.4 between the photometric measurements and the spectroscopic benchmark environments. This is sufficient to extract an environment signal from large scale photometric surveys. The second study in this thesis is based on the science verification data from the DES. This is the first set of observations from the survey. This study uses ∼3.2 million galaxies from the SPT-East (South Pole Telescope) field that covers approximately 100 sq. deg. of the sky. From the grizY photometry the analysis pipeline is used to derive galaxy stellar masses and absolute magnitudes. The errors on these properties are assessed using Monte-Carlo simulations sampled from the full photometric redshift probability distributions. Galaxy environments are computed using a fixed conical aperture method, for a range of scales. Galaxy environment probability distribution functions are constructed and the dependence of the environment errors on the aperture parameters is investigated. The environment components of the galaxy stellar mass function for the redshift range: 0.15 < z < 1.05 are calculated. For z < 0.75 it is found that the fraction of massive galaxies is larger in high density environment than low density environments. The low and high density components converge with increasing redshift to z ∼ 1.0 where the shapes of the mass function components are indistinguishable. This redshift is important because it marks the transition between an earlier epoch where the mass distribution of galaxies is independent of environment and a later epoch where the mass distribution does depend on galaxy environment. This study shows the build up of high density structures around massive galaxies, through cosmic time. The results in this thesis demonstrate that large scale photometric surveys can produce competitive galaxy evolution science, enabling further investigations of the role of galaxy environment. This is hugely encouraging for current and future experiments.

With the substantial improvement in instrumentation and our ability to now probe ever greater regions of space, the study of the Universe in its totality has moved towards the regime of a precision discipline. Several probes are now used by cosmologists to study the underlying cosmological model and understand its constituents. Modern cosmology has honed in on a concordance model that tells us that the Universe is predominantly composed of ‘dark’ components which still remain elusive to discovery. Weak lensing has emerged as one such powerful tool in probing the cosmological model. Its clean application of General Relativity, as well as its insensitivity in distinguishing between luminous and ‘dark matter' make it an attractive probe of the large scale structure in the Universe. To date, almost all weak lensing studies have been conducted using optical data. This is due primarily to the constraints required for a weak lensing study, i.e. high angular resolution and a high number density of distant sources, being most readily met at these wavelengths. The primary goal of this thesis is to address the feasibility of conducting such weak lensing experiments at the much longer, radio wavelengths. Many of the existing radio facilities are either undergoing (e.g. Extended Multi-Element Radio Linked Interferometer (eMERLIN1), Expanded Very Large Array (EVLA2)) or are scheduled to undergo major upgrades resulting in them being able to provide high resolution and high sensitivity data over a large field-of-view; aiding greatly in the detection of many more galaxies, a primary goal for weak lensing. Coupled with this, new, large interferometric arrays (e.g. Low Frequency Array (LOFAR3), and eventually the Square Kilometre Array (SKA4)) are in the process of being built and they too will provide the necessary quality of data for weak lensing experiments.

In this dissertation, we explore the cosmological sensitivity of well-motivated extensions of the Standard Model (SM) of particles. We focus on two specific models, the vector portal and the Higgs portal, that can connect the SM to a dark sector of new hidden particles. We find that both portals have sensitivity in the ultra-weak coupling regime, where the relic abundance is set by the freeze-in mechanism. Provided that the mediators of the portal interactions decay into the SM, we derive the constraints on masses and couplings of such states from precision cosmology. As a primary source of constraints, we use Big Bang Nucleosynthesis (BBN), the Cosmic Microwave Background (CMB) and the diffuse X-ray background. For the Higgs portal scalar, we improve the relic abundance calculation in the literature and provide an estimate of thermal corrections to the freeze-in yield. We find that the cosmological bounds are relatively insensitive to improvements in the abundance accuracy, and a full finite-temperature calculation is not needed. We also investigate the BBN constraints for hypothetical long-lived metastable scalars particles $S$ that can be produced at the Large Hadron Collider from decays of the Higgs boson. We find that for viable branching ratios Br($h \to SS$), the early universe metastable abundance of $S$, regulated by its self-annihilation through the Higgs portal, is so large that the lifetime of $S$ is strongly constrained to $\tau_S < 0.1$~s to maintain the consistency of BBN predictions with observations. This provides a useful upper bound on the lifetimes of $S$ particles that a purposely-built detector, such as the one suggested in the MATHUSLA proposal, seek to discover. We also investigate the viability and detectability of freeze-in self-interacting fermionic dark matter communicating with the SM via a vector portal. We focus on the parameter where the $\chi \bar{\chi} \to A'A'$ is negligible, as required by a variety of indirect detection constraints. We find that planned upgrades to the direct detection experiments will be able to probe the region of parameter space that can alleviate small scale structure problems of dark matter via self-interactions for a dark fine structure constant as small as $\alpha_d =10^{-4}$. We forecast the sensitivity for Lux-ZEPLIN, XENONnT and PandaX-4T. / Graduate

In this thesis I discuss my work on the Arcminute Microkelvin Imager (AMI). I focus on the detection of Sunyaev-Zel'dovich (SZ) signatures at 14-18GHz. Once the background science and operation of the instrument are described I proceed to present my contribution to the calibration of AMI, including: primary beam measurements; refinements to the known antenna geometry and flagging geostationary satellite interference. This is followed by an outline of the software that I have developed to subtract sources from visibilities, concatenate data from multiple observations, simulate data, and perform jack-knife tests to evaluate the magnitude of systematic errors. The Bayesian analysis that I use to obtain parameter estimates and to quantify the significance of putative SZ detections is described. I perform realistic simulations of clusters and use these to characterisethe analysis. I then, for the first time, apply the analysis to data from the AMI blind cluster survey. I identify several previously unknownSZ decrements. Finally, I conduct pointed observations towards a high luminosity subsample of eight clusters from the Local Cluster Substructure Survey(LoCuSS). For each of these I provide probability distributions of parameters such as mass, radius, and temperature. I compare myresults to those in the literature and find an overall agreement.

Nonstandard cosmological models of two broad classes are examined: those in which there are more than four spacetime dimensions, and those in which there is a variable cosmological “constant” Λ. We test claims that a number of higher-dimensional models give rise to inflation. New constraints are placed on such models, and a number of them are ruled out. We then investigate the potential of variable-Λ theories to address the problem of the initial singularity. We consider a number of different phenomenological representations for this parameter, assessing their implications for the evolution of the cosmological scale factor as well as a range of observational data. In several cases we find nonsingular models which are compatible with observation. / Graduate

Bibliography: pages 112-113. / This thesis discusses the Sachs-Wolfe effect, which is the variation in the observed temperature of radiation emitted at the last scattering surface which occurs at the place where matter and radiation decouple at about 4000 degrees Kelvin. The work is in two parts, with the first part dealing with extensions made by George Ellis, Chongming Xu, Bill Stoeger and myself to the paper by Miroslaw Panek [13] where the gauge invariant formalism of cosmological density perturbations by James Bardeen [1] has been used to find the SW effect in the case of a perturbed Friedman-Lemaitre-Robertson-Walker (FLRW) universe with a barotropic equation of state describing the matter in the unperturbed case. In our work we extend the example given by Panek for a flat universe (K = 0) filled with dust where the density perturbations are adiabatic, to the case of non-fl.at universes (K = -1, 0 + 1) filled with a mixture of N types of matter where the density perturbations are nonadiabatic. The second part shows the agreement between the formalisms of Sachs and Wolfe's pioneering paper and the recent work of George Ellis and Marco Bruni which presents the study of cosmological perturbations in a gauge invariant and covariant way. After the overview of the work covered in this thesis, the gauge invariant formulation of Bardeen is discussed where we follow the description by Panek of a universe whose energy content is described by a mixture of N ideal fluids coupled only by gravity. From the Einstein equations we get Bardeen's evolution equation for the gauge invariant energy density perturbation which is now given for the N different matter fluids as it appears in Panek. We then checked Panek's equations where he finds an expression for the placing of the perturbed last scattering surface, after which he derives an equation for the fractional temperature variation and writes it in terms of the perturbation variables. The equation found by SW for their particular choice of K = O, pressure free dust, where the last scattering surface is placed at its unperturbed position, is verified in terms of the Bardeen formalism. Now we extend this simple case to nonadiabatic perturbations in the same scenario and find the SW effect for a mixture of two fluids: dust and radiation, with nonadiabatic perturbations in a not necessarily flat universe. We then generalise to the case of a mixture or baryons and radiation and N types of matter. This section then ends with a calculation of the difference between temperatures taken from two different directions in the sky and is written in terms of the fractional temperature perturbation defined by Panek. The second part puts forward the formulation of the gauge problem by Ellis and Bruni (EB), and then writes out their gauge invariant quantities in terms of the SW variables. Their evolution equations are verified in this form, and the shear and vorticity determined as well. Now all of the EB cosmological quantities are listed for the special gauge that SW use and then we explore the relation between the SW metric and that of Bardeen before ending off by verifying that the form for the redshift in the EB approach is in agreement with that given by Panek.

Includes bibliographical references. / A generic feature of most inflationary scenarios is the generation of primordial perturbations. Ordinarily, such perturbations can interact with a weak magnetic field in a plasma, resulting in a wide range of phenomena, such as the parametric excitation of plasma waves by gravitational waves. This mechanism has been studied in different contexts in the literature, such as the possibility of indirect detection of gravitational waves through electromagnetic signatures of the interaction. In this work, we consider this concept in the particular case of magnetic field amplification. Specifically, we use non-linear gauge-in variant perturbation theory to study the interaction of a primordial seed magnetic field with density and gravitational wave perturbations in an almost Friedmann-Lemaıtre-Robertson- Walker (FLRW) spacetime with zero spatial curvature. We compare the effects of this coupling under the assumptions of poor conductivity, perfect conductivity and the case where the electric field is sourced via the coupling of velocity perturbations to the seed field in the ideal magnetohydrodynamic (MHD) regime, thus generalizing, improving on and correcting previous results. We solve our equations for long wavelength limits and numerically integrate the resulting equations to generate power spectra for the electromagnetic field variables, showing where the modes cross the horizon. We find that the interaction can seed Electric fields with non-zero curl and that the curl of the electric field dominates the power spectrum on small scales, in agreement with previous arguments. The second focus area of the thesis is the development a stable high order mesh refinement scheme for the solution of hyperbolic partial differential equations. It has now become customary in the field of numerical relativity to couple high order finite difference schemes to mesh refinement algorithms. This approach combines the efficiency of local mesh refinement with the robustness and accuracy of higher order methods. To this end, different modifications of the standard Berger-Oliger adaptive mesh refinement a logarithm have been proposed. In this work we present a new fourth order convergent mesh refinement scheme with sub- cycling in time for numerical relativity applications. One of the distinctive features of our algorithm is that we do not use buffer zones to deal with refinement boundaries, as is currently done in the literature, but explicitly specify boundary data for refined grids instead. We argue that the incompatibility of the standard mesh refinement algorithm with higher order Runge Kutta methods is a manifestation of order reduction phenomena which is caused by inconsistent application of boundary data in the refined grids. Indeed, a peculiar feature of high order explicit Runge Kutta schemes is that they behave like low order schemes when applied to hyperbolic problems with time dependent Dirichlet boundary conditions. We present a new algorithm to deal with this phenomenon and through a series of examples demonstrate fourth order convergence. Our scheme also addresses the problem of spurious reflections that are generated when propagating waves cross mesh refinement boundaries. We introduce a transition zone on refined levels within which the phase velocity of propagating modes is allowed to decelerate in order to smoothly match the phase velocity of coarser grids. We apply the method to test problems involving propagating waves and show a significant reduction in spurious reflections.