We determine the mass scale ofPlanckgalaxy clusters using gravitational lensing mass measurements from the Cluster Lensing And Supernova survey withHubble(CLASH). We have compared the lensing masses to thePlanckSunyaev-Zeldovich (SZ) mass proxy for 21 clusters in common, employing a Bayesian analysis to simultaneously fit an idealized CLASH selection function and the distribution between the measured observables and true cluster mass. We used a tiered analysis strategy to explicitly demonstrate the importance of priors on weak lensing mass accuracy. In the case of an assumed constant bias,b_SZ, between true cluster mass,M₅₀₀, and thePlanckmass proxy,M_PL, our analysis constrains 1−b_SZ= 0.73 ± 0.10 when moderate priors on weak lensing accuracy are used, including a zero-mean Gaussian with standard deviation of 8% to account for possible bias in lensing mass estimations. Our analysis explicitly accounts for possible selection bias effects in this calibration sourced by the CLASH selection function. Our constraint on the cluster mass scale is consistent with recent results from the Weighing the Giants program and the Canadian Cluster Comparison Project. It is also consistent, at 1.34σ, with the value needed to reconcile thePlanckSZ cluster counts withPlanck’s base ΛCDM model fit to the primary cosmic microwave background anisotropies.

The energy conditions play an important role in the understanding of several properties of the Universe, including the current accelerating expansion phase and the possible existence of the so-called phantom fields. We show that the integrated bounds provided by the energy conditions on cosmological observables such as the distance modulus $\mu (z)$ and the lookback time $t_L(z)$ are not sufficient (or necessary) to ensure the local fulfillment of the energy conditions, making explicit the limitation of these bounds in the confrontation with observational data. We recast the energy conditions as bounds on the deceleration and normalized Hubble parameters, obtaining new bounds which are necessary and sufficient for the local fulfillment of the energy conditions. A statistical confrontation, with $1\sigma -3\sigma$ confidence levels, between our bounds and supernovae data from the gold and combined samples is made for the recent past. Our analyses indicate, with $3\sigma$ confidence levels, the fulfillment of both the weak energy condition ($\mathbf{W}\mathbf{E}\mathbf{C}$) and dominant energy condition ($\mathbf{D}\mathbf{E}\mathbf{C}$) for $z\le 1$ and $z\lesssim 0.8$, respectively. In addition, they suggest a possible recent violation of the null energy condition ($\mathbf{N}\mathbf{E}\mathbf{C}$) with $3\sigma$, i.e. a very recent phase of superacceleration. Our analyses also show the possibility of violation of the strong energy condition ($\mathbf{S}\mathbf{E}\mathbf{C}$) with $3\sigma$ in the recent past ($z\le 1$), but interestingly the $q(z)$-best-fit curve crosses the $\mathbf{S}\mathbf{E}\mathbf{C}$—fulfillment divider at $z\simeq 0.67$, which is a value very close to the beginning of the epoch of cosmic acceleration predicted by the standard concordance flat $\Lambda \mathrm{CDM}$ scenario.

Sunyaev-Zel'dovich (SZ) surveys are promising probes of cosmology — in particular for Dark Energy (DE) —, given their ability to find distant clusters and provide estimates for their mass. However, current SZ catalogs contain tens to hundreds of objects and maximum likelihood estimators may present biases for such sample sizes. In this work we study estimators from cluster abundance for some cosmological parameters, in particular the DE equation of state parameter w₀, the amplitude of density fluctuations σ₈, and the Dark Matter density parameter Ω_c. We begin by deriving an unbinned likelihood for cluster number counts, showing that it is equivalent to the one commonly used in the literature. We use the Monte Carlo approach to determine the presence of bias using this likelihood and study its behavior with both the area and depth of the survey, and the number of cosmological parameters fitted. Our fiducial models are based on the South Pole Telescope (SPT) SZ survey. Assuming perfect knowledge of mass and redshift some estimators have non-negligible biases. For example, the bias of σ₈ corresponds to about 40% of its statistical error bar when fitted together with Ω_c and w₀. Including a SZ mass-observable relation decreases the relevance of the bias, for the typical sizes of current SZ surveys. Considering a joint likelihood for cluster abundance and the so-called ``distance priors'', we obtain that the biases are negligible compared to the statistical errors. However, we show that the biases from SZ estimators do not go away with increasing sample sizes and they may become the dominant source of error for an all sky survey at the SPT sensitivity. Finally, we compute the confidence regions for the cosmological parameters using Fisher matrix and profile likelihood approaches, showing that they are compatible with the Monte Carlo ones. The results of this work validate the use of the current maximum likelihood methods for present SZ surveys, but highlight the need for further studies for upcoming experiments. To perform the analyses of this work, we developed fast, accurate, and adaptable codes for cluster counts in the framework of the Numerical Cosmology Library.

The problem of finding a vacuum definition for a single quantum field in curved spacetimes is discussed under a new geometrical perspective. The phase space dynamics of the quantum field modes are mapped to curves in a two-dimensional hyperbolic metric space, in which distances between neighbor points are shown to be proportional to the Bogoliubov coefficients associated with their corresponding mode solutions in phase space. The vacuum state for each mode is then defined as the unique trajectory from which all mapped phase space solutions move within thin annular regions around it. This property implies the stability of the vacuum state: solutions evolved from a point in this trajectory stay close to it as both evolve, and the particle creation is therefore minimized. The new approach is applied to the well-known cases of the time-independent dynamics, where the solutions draw circles around this curve, and to the time-dependent dynamics where adiabatic approximation is valid. Additionally, our analysis is extended to more challenging cases of time-dependent dynamics, where the adiabatic approximation is not possible, such as in the super-Hubble or low frequency regimes. It is shown that stability trajectories can also be found in these situations, and stable quantum vacua can be obtained. This new formalism is applied to two situations: de Sitter space, where the Bunch-Davies vacuum is obtained in a completely different manner through an analysis in the super-Hubble regime, and in the context of cosmological bouncing models, in which the contracting phase is dominated by a cosmological constant in the asymptotic past. A new vacuum state for cosmological perturbations is proposed in this situation.