Excursion Set Halo Mass Function and Bias in a Stochastic Barrier Model of Ellipsoidal Collapse

We use the Excursion Set formalism to compute the properties of the halo mass distribution for a stochastic barrier model which encapsulates the main features of the ellipsoidal collapse of dark matter halos. Non-markovian corrections due to the sharp filtering of the linear density field in real space are computed with the path-integral technique introduced by Maggiore & Riotto (2010). Here, we provide a detailed derivation of the results presented in Corasaniti & Achitouv (2011) and extend the mass function analysis to higher redshift. We also derive an analytical expression for the linear halo bias. We find the analytically derived mass function to be in remarkable agreement with N-body simulation data from Tinker et al. (2008) with differences smaller than ~5% over the range of mass probed by the simulations. The excursion set solution from Monte Carlo generated random walks shows the same level of agreement, thus confirming the validity of the path-integral approach for the barrier model considered here. Similarly the analysis of the linear halo bias shows deviations no greater than 20%. Overall these results indicate that the Excursion Set formalism in combination with a realistic modeling of the conditions of halo collapse can provide an accurate description of the halo mass distribution.Comment: 16 pages, 9 figures; companion paper published in PRL 106 (2011) 241302. To appear on PR

Constraining the quintessence equation of state with SnIa data and CMB peaks

Quintessence has been introduced as an alternative to the cosmological constant scenario to account for the current acceleration of the universe. This new dark energy component allows values of the equation of state parameter $w_{Q}^0\geq-1$, and in principle measurements of cosmological distances to Type Ia supernovae can be used to distinguish between these two types of models. Assuming a flat universe, we use the supernovae data and measurements of the position of the acoustic peaks in the Cosmic Microwave Background (CMB) spectra to constrain a rather general class of Quintessence potentials, including inverse power law models and recently proposed Supergravity inspired potentials. In particular we use a likelihood analysis, marginalizing over the dark energy density $\Omega_{Q}$, the physical baryon density $\Omega_{b}h^2$ and the scalar spectral index $n$, to constrain the slopes of our Quintessence potential. Considering only the first Doppler peak the best fit in our range of models gives $w_{Q}^0\sim-0.8$. However, including the SnIa data and the three peaks, we find an upper limit on the present value of the equation of state parameter, $-1\leq w_{Q}^0\leq-0.93$ at $2\sigma$, a result that appears to rule out a class of recently proposed potentials.Comment: Accepted for pubblication in PRD, 7 pages, 6 figures. New revised analysi

Signals of primordial phase transitions on CMB maps

The analysis of the CMB anisotropies is a rich source of cosmological informations. In our study, we simulated the signals produced by the relics of a first order phase transition occured during an inflationary epoch in the early Universe. These relics are bubbles of true vacuum that leave a characteristic non-Gaussian imprint on the CMB. We use different statistical estimators in order to evaluate this non-Gaussianity. We obtain some limits on the allowed values of the bubble parameters comparing our results with the experimental data. We also predict the possibility to detect this signal with the next high resolution experiments.Comment: 2 pages, submitted to Proceedings of 9th Marcel Grossmann meetin

Present limits to cosmic bubbles from the COBE-DMR three point correlation function

The existence of large scale voids in several galaxy surveys suggests the occurence of an inflationary first order phase transition. This process generates primordial bubbles that, before evolving into the present voids, leave at decoupling a non-Gaussian imprint on the CMB. I this paper we evaluate an analytical expression of the collapsed three point correlation function from the bubble temperature fluctuations. Comparing the results with COBE-DMR measures, we obtain upper limits on the allowed non-Gaussianity and hence on the bubble parameters.Comment: 4 pages, 3 figures; submitted to MNRA

Extending the Coyote emulator to dark energy models with standard w0w_0-waw_a parametrization of the equation of state

We discuss an extension of the Coyote emulator to predict non-linear matter power spectra of dark energy (DE) models with a scale factor dependent equation of state of the form w = w_0 + ( 1 - a )w_a . The extension is based on the mapping rule between non-linear spectra of DE models with constant equation of state and those with time varying one originally introduced in ref. [40]. Using a series of N-body simulations we show that the spectral equivalence is accurate to sub-percent level across the same range of modes and redshift covered by the Coyote suite. Thus, the extended emulator provides a very efficient and accurate tool to predict non-linear power spectra for DE models with w_0 - w_a parametrization. According to the same criteria we have developed a numerical code, and we have implemented in a dedicated module for the CAMB code, that can be used in combination with the Coyote Emulator in likelihood analyses of non-linear matter power spectrum measurements. All codes can be found at https://github.com/luciano-casarini/PKequalComment: All codes can be found at https://github.com/luciano-casarini/PKequa

An indirect limit on the amplitude of primordial Gravitational Wave Background from CMB-Galaxy Cross Correlation

While large scale cosmic microwave background (CMB) anisotropies involve a combination of the scalar and tensor fluctuations, the scalar amplitude can be independently determined through the CMB-galaxy cross-correlation. Using recently measured cross-correlation amplitudes, arising from the cross-correlation between galaxies and the Integrated Sachs Wolfe effect in CMB anisotropies, we obtain a constraint r < 0.5 at 68% confidence level on the tensor-to-scalar fluctuation amplitude ratio. The data also allow us to exclude gravity waves at a level of a few percent, relative to the density field, in a low - Lambda dominated universe(Omega_Lambda~0.5). In future, joining cross-correlation ISW measurements, which captures cosmological parameter information, with independent determinations of the matter density and CMB anisotropy power spectrum, may constrain the tensor-to-scalar ratio to a level above 0.05. This value is the ultimate limit on tensor-to-scalar ratio from temperature anisotropy maps when all other cosmological parameters except for the tensor amplitude are known and the combination with CMB-galaxy correlation allows this limit to be reached easily by accounting for degeneracies in certain cosmological parameters.Comment: 5 Pages, 1 Figure, revised discussion on cosmic variance limits on the tensor-to-scalar ratio from CMB, matches PRD accepted versio

Self-consistency of the Excursion Set Approach

The excursion set approach provides a framework for predicting how the abundance of dark matter halos depends on the initial conditions. A key ingredient of this formalism comes from the physics of halo formation: the specification of a critical overdensity threshold (barrier) which protohalos must exceed if they are to form bound virialized halos at a later time. Another ingredient is statistical, as it requires the specification of the appropriate statistical ensemble over which to average when making predictions. The excursion set approach explicitly averages over all initial positions, thus implicitly assuming that the appropriate ensemble is that associated with randomly chosen positions in space, rather than special positions such as peaks of the initial density field. Since halos are known to collapse around special positions, it is not clear that the physical and statistical assumptions which underlie the excursion set approach are self-consistent. We argue that they are at least for low mass halos, and illustrate by comparing our excursion set predictions with numerical data from the DEUS simulations.Comment: 5 pages, 2 figure

Toward a Universal Formulation of the Halo Mass Function

We compute the dark matter halo mass function using the excursion set formalism for a diffusive barrier with linearly drifting average which captures the main features of the ellipsoidal collapse model. We evaluate the non-Markovian corrections due to the sharp filtering of the linear density field in real space with a path-integral method. We find an unprecedented agreement with N-body simulation data with deviations within ~5% level over the range of masses probed by the simulations. This indicates that the Excursion Set in combination with a realistic modelling of the collapse threshold can provide a robust estimation of the halo mass function.Comment: 5 pages, 2 figures; substantial corrections, results unchanged. Matches PRL published versio