Diego Blas

Cosmological perturbation theory at three-loop order

We analyze the dark matter power spectrum at three-loop order in standard perturbation theory of large scale structure. We observe that at late times the loop expansion does not converge even for large scales (small momenta) well within the linear regime, but exhibits properties compatible with an asymptotic series. We propose a technique to restore the convergence in the limit of small momentum, and use it to obtain a perturbative expansion with improved convergence for momenta in the range where baryonic acoustic oscillations are present. Our numerical three-loop results are compared with data from N-body simulations at different redshifts, and we find good agreement within this range.

Renormalization of Hořava gravity

We prove perturbative renormalizability of projectable Horava gravity. The key element of the argument is the choice of a gauge which ensures the correct anisotropic scaling of the propagators and their uniform falloff at large frequencies and momenta. This guarantees that the counterterms required to absorb the loop divergences are local and marginal or relevant with respect to the anisotropic scaling. Gauge invariance of the counterterms is achieved by making use of the background-covariant formalism. We also comment on the difficulties of this approach when addressing the renormalizability of the nonprojectable model.

On the non-linear scale of cosmological perturbation theory

We discuss the convergence of cosmological perturbation theory. We prove that the polynomial enhancement of the non-linear corrections expected from the effects of soft modes is absent in equal-time correlators like the power or bispectrum. We first show this at leading order by resumming the most important corrections of soft modes to an arbitrary skeleton of hard fluctuations. We derive the same result in the eikonal approximation, which also allows us to show the absence of enhancement at any order. We complement the proof by an explicit calculation of the power spectrum at two-loop order, and by further numerical checks at higher orders. Using these insights, we argue that the modification of the power spectrum from soft modes corresponds at most to logarithmic corrections at any order in perturbation theory. Finally, we discuss the asymptotic behavior in the large and small momentum regimes and identify the expansion parameter pertinent to non-linear corrections.

Testing Lorentz invariance of dark matter

We study the possibility to constrain deviations from Lorentz invariance in dark matter (DM) with cosmological observations. Breaking of Lorentz invariance generically introduces new light gravitational degrees of freedom, which we represent through a dynamical timelike vector field. If DM does not obey Lorentz invariance, it couples to this vector field. We find that this coupling affects the inertial mass of small DM halos which no longer satisfy the equivalence principle. For large enough lumps of DM we identify a (chameleon) mechanism that restores the inertial mass to its standard value. As a consequence, the dynamics of gravitational clustering are modified. Two prominent effects are a scale dependent enhancement in the growth of large scale structure and a scale dependent bias between DM and baryon density perturbations. The comparison with the measured linear matter power spectrum in principle allows to bound the departure from Lorentz invariance of DM at the per cent level.

Phenomenology of theories of gravity without Lorentz invariance: The preferred frame case

Theories of gravitation without Lorentz invariance are candidates of low-energy descriptions of quantum gravity. In this paper, we will describe the phenomenological consequences of the candidates associated to the existence of a preferred time direction.

Cosmological constraints on Lorentz violating dark energy

The role of Lorentz invariance as a fundamental symmetry of nature has been lately reconsidered in different approaches to quantum gravity. It is thus natural to study whether other puzzles of physics may be solved within these proposals. This may be the case for the cosmological constant problem. Indeed, it has been shown that breaking Lorentz invariance provides Lagrangians that can drive the current acceleration of the universe without experiencing large corrections from ultraviolet physics. In this work, we focus on the simplest model of this type, called Theta CDM, and study its cosmological implications in detail. At the background level, this model cannot be distinguished from Lambda CDM. The differences appear at the level of perturbations. We show that in Theta CDM, the spectrum of CMB anisotropies and matter fluctuations may be affected by a rescaling of the gravitational constant in the Poisson equation, by the presence of extra contributions to the anisotropic stress, and finally by the existence of extra clustering degrees of freedom. To explore these modifications accurately, we modify the Boltzmann code class. We then use the parameter inference code MONTE PYTHON to confront Theta CDM with data from WMAP-7, SPT and WiggleZ. We obtain strong bounds on the parameters accounting for deviations from Lambda CDM. In particular, we find that the discrepancy between the gravitational constants appearing in the Poisson and Friedmann equations is constrained at the level of 1.8%.

Structure formation with massive neutrinos: going beyond linear theory

We compute non-linear corrections to the matter power spectrum taking the time- and scale-dependent free-streaming length of neutrinos into account. We adopt a hybrid scheme that matches the full Boltzmann hierarchy to an effective two-fluid description at an intermediate redshift. The non-linearities in the neutrino component are taken into account by using an extension of the time-flow framework. We point out that this remedies a spurious behaviour that occurs when neglecting non-linear terms for neutrinos. This behaviour is related to how efficiently short modes decouple from long modes and can be traced back to the violation of momentum conservation if neutrinos are treated linearly. Furthermore, we compare our results at next to leading order to various other methods and quantify the accuracy of the fluid description. Due to the correct decoupling behaviour of short modes, the two-fluid scheme is a suitable starting point to compute higher orders in perturbations or for resummation methods.

Cosmological constraints on deviations from Lorentz invariance in gravity and dark matter

We consider a scenario where local Lorentz invariance is violated by the existence of a preferred time direction at every space-time point. This scenario can arise in the context of quantum gravity and its description at low energies contains a unit time-like vector field which parameterizes the preferred direction. The particle physics tests of Lorentz invariance preclude a direct coupling of this vector to the fields of the Standard Model, but do not bear implications for dark matter. We discuss how the presence of this vector and its possible coupling to dark matter affect the evolution of the Universe. At the level of homogeneous cosmology the only effect of Lorentz invariance violation is a rescaling of the expansion rate. The physics is richer at the level of perturbations. We identify three effects crucial for observations: the rescaling of the matter contribution to the Poisson equation, the appearance of an extra contribution to the anisotropic stress and the scale-dependent enhancement of dark matter clustering. These effects result in distinctive features in the power spectra of the CMB and density fluctuations. Making use of the data from Planck and WiggleZ we obtain the most stringent cosmological constraints to date on departures from Lorentz symmetry. Our analysis provides the first direct bounds on deviations from Lorentz invariance in the dark matter sector.

Large scale structure from viscous dark matter

Cosmological perturbations of sufficiently long wavelength admit a fluid dynamic description. We consider modes with wavevectors below a scale

Ultralight Dark Matter Resonates with Binary Pulsars

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