Spacetimes with horizons show a resemblance to thermodynamic systems and one can associate the notions of temperature and entropy with them. In the case of Einstein-Hilbert gravity, it is possible to interpret Einstein's equations as the thermodynamic identity T dS = dE + P dV for a spherically symmetric spacetime and thus provide a thermodynamic route to understand the dynamics of gravity. We study this approach further and show that the field equations for LanczosLovelock action in a spherically symmetric spacetime can also be expressed as T dS = dE +P dV with S and E being given by expressions previously derived in the literature by other approaches. The Lanczos-Lovelock Lagrangians are of the form L = Q bcd a R a bcd with ∇ b Q bcd a = 0. In such models, the expansion of Q bcd a in terms of the derivatives of the metric tensor determines the structure of the theory and higher order terms can be interpreted quantum corrections to Einstein gravity. Our result indicates a deep connection between the thermodynamics of horizons and the allowed quantum corrections to standard Einstein gravity, and shows that the relation T dS = dE + P dV has a greater domain of validity that Einstein's field equations.

The null surfaces of a spacetime act as one-way membranes and can block information for a corresponding family of observers (time-like curves). Since lack of information can be related to entropy, this suggests the possibility of assigning an entropy to the null surfaces of a spacetime. We motivate and introduce such an entropy functional for any vector field in terms of a fourth-rank divergence free tensor P cd ab with the symmetries of the curvature tensor. Extremising this entropy for all the null surfaces then leads to equations for the background metric of the spacetime. When P cd ab is constructed from the metric alone, these equations are identical to Einstein's equations with an undetermined cosmological constant (which arises as an integration constant). More generally, if P cd ab is allowed to depend on both metric and curvature in a polynomial form, one recovers the Lanczos-Lovelock gravity. In all these cases: (a) We only need to extremise the entropy associated with the null surfaces; the metric is not a dynamical variable in this approach. (b) The extremal value of the entropy agrees with standard results, when evaluated on-shell for a solution admitting a horizon. The role of full quantum theory of gravity will be to provide the specific form of P cd ab which should be used in the entropy functional. With such an interpretation, it seems reasonable to interpret the Lanczos-Lovelock type terms as quantum corrections to classical gravity.

We describe how to extend the excursion set peaks framework so that its predictions of dark halo abundances and clustering can be compared directly with simulations. These extensions include: a halo mass definition which uses the TopHat filter in real space; the mean dependence of the critical density for collapse δ c on halo mass m; and the scatter around this mean value. All three of these are motivated by the physics of triaxial rather than spherical collapse. A comparison of the resulting mass function with N -body results shows that, if one uses δ c (m) and its scatter as determined from simulations, then all three are necessary ingredients for obtaining ∼ 10% accuracy. E.g., assuming a constant value of δ c with no scatter, as motivated by the physics of spherical collapse, leads to many more massive halos than seen in simulations. The same model is also in excellent agreement with N -body results for the linear halo bias, especially at the high mass end where the traditional peak-background split argument applied to the mass function fit is known to underpredict the measured bias by ∼ 10%. In the excursion set language, our model is about walks centered on special positions (peaks) in the initial conditions -we discuss what it implies for the usual calculation in which all walks contribute to the statistics.

We investigate the possible occurrence of a positive cosmic acceleration in a spatially averaged, expanding, unbound Lemaître-Tolman-Bondi cosmology. By studying an approximation in which the contribution of three-curvature dominates over the matter density, we construct numerical models which exhibit acceleration. *

We study the role of the local tidal environment in determining the assembly bias of dark matter haloes. Previous results suggest that the anisotropy of a halo's environment (i.e, whether it lies in a filament or in a more isotropic region) can play a significant role in determining the eventual mass and age of the halo. We statistically isolate this effect using correlations between the large-scale and small-scale environments of simulated haloes at z = 0 with masses between 10 11.6 (m/h −1 M ) 10 14.9 . We probe the large-scale environment using a novel halo-by-halo estimator of linear bias. For the small-scale environment, we identify a variable α R that captures the tidal anisotropy in a region of radius R = 4R 200b around the halo and correlates strongly with halo bias at fixed mass. Segregating haloes by α R reveals two distinct populations. Haloes in highly isotropic local environments (α R 0.2) behave as expected from the simplest, spherically averaged analytical models of structure formation, showing a negative correlation between their concentration and large-scale bias at all masses. In contrast, haloes in anisotropic, filament-like environments (α R 0.5) tend to show a positive correlation between bias and concentration at any mass. Our multi-scale analysis cleanly demonstrates how the overall assembly bias trend across halo mass emerges as an average over these different halo populations, and provides valuable insights towards building analytical models that correctly incorporate assembly bias. We also discuss potential implications for the nature and detectability of galaxy assembly bias.

To shed light on the fundamental problems posed by dark energy and dark matter, a large number of experiments have been performed and combined to constrain cosmological models. We propose a novel way of quantifying the information gained by updates on the parameter constraints from a series of experiments which can either complement earlier measurements or replace them. For this purpose, we use the Kullback-Leibler divergence or relative entropy from information theory to measure differences in the posterior distributions in model parameter space from a pair of experiments. We apply this formalism to a historical series of cosmic microwave background experiments ranging from Boomerang to WMAP, SPT, and Planck. Considering different combinations of these experiments, we thus estimate the information gain in units of bits and distinguish contributions from the reduction of statistical errors and the "surprise" corresponding to a significant shift of the parameters' central values. For this experiment series, we find individual relative entropy gains ranging from about 1 to 30 bits. In some cases, e.g. when comparing WMAP and Planck results, we find that the gains are dominated by the surprise rather than by improvements in statistical precision. We discuss how this technique provides a useful tool for both quantifying the constraining power of data from cosmological probes and detecting the tensions between experiments.

We extend the Halo Occupation Distribution (HOD) framework to generate mock galaxy catalogs exhibiting varying levels of "galactic conformity", which has emerged as a potentially powerful probe of environmental effects in galaxy evolution. Our model correlates galaxy colours in a group with the concentration of the common parent dark halo through a "group quenching efficiency" ρ which makes older, more concentrated halos at fixed mass preferentially host redder galaxies. We find that, for a specific value of ρ, this 1-halo conformity matches corresponding measurements in a group catalog based on the Sloan Digital Sky Survey. Our mocks also display conformity at large separations from isolated objects, potentially an imprint of halo assembly bias. A detailed study -using mocks with assembly bias erased while keeping 1-halo conformity intact -reveals a rather nuanced situation, however. At separations 4Mpc, conformity is mainly a 1-halo effect dominated by the largest halos and is not a robust indicator of assembly bias. Only at very large separations ( 8Mpc) does genuine 2-halo conformity, driven by the assembly bias of small halos, manifest distinctly. We explain all these trends in standard Halo Model terms. Our model opens the door to parametrized HOD analyses that self-consistently account for galactic conformity at all scales.

The internal properties of dark matter haloes correlate with the large-scale halo clustering strength at fixed halo mass – an effect known as assembly bias – and are also strongly affected by the local, non-linear cosmic web. Characterizing a halo’s local web environment by its tidal anisotropy α at scales approximately four times the halo radius, we demonstrate that these multiscale correlations represent two distinct statistical links: one between the internal property and α, and the other between α and large-scale (${\gtrsim}30\, h^{-1}\, {\rm Mpc}$) halo bias b1. We focus on scalar internal properties of haloes related to formation time (concentration cvir), shape (mass ellipsoid asphericity c/a), velocity dispersion structure (velocity ellipsoid asphericity cv/av and velocity anisotropy β), and angular momentum (dimensionless spin λ) in the mass range $8\times 10^{11}\lesssim M_{\rm vir}/(\, h^{-1}\, \mathrm{M}_{\odot })\lesssim 5\times 10^{14}$. Using conditional correlation coefficients and other detailed tests, we show that the joint distribution of α, b1, and any of the internal properties c ∈ {β, cv/av, c/a, cvir, λ} is consistent with p(α, b1, c) ≃ p(α)p(b1|α)p(c|α), at all but the largest masses. Thus, the assembly bias trends c↔b1 reflect the two fundamental correlations c↔α and b1↔α. Our results are unaffected by the exclusion of haloes with recent major merger events or splashback objects, although the latter are distinguished by the fact that α does not explain their assembly bias trends. The overarching importance of α provides a new perspective on the nature of assembly bias of distinct haloes, with potential ramifications for incorporating realistic assembly bias effects into mock catalogues of future large-scale structure surveys and for detecting galaxy assembly bias.