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Olmo, G. J., & Rubiera-Garcia, D. (2013). Importance of torsion and invariant volumes in Palatini theories of gravity. Phys. Rev. D, 88(8), 084030–11pp.
Abstract: We study the field equations of extensions of general relativity formulated within a metric-affine formalism setting torsion to zero (Palatini approach). We find that different (second-order) dynamical equations arise depending on whether torsion is set to zero (i) a priori or (ii) a posteriori, i.e., before or after considering variations of the action. Considering a generic family of Ricci-squared theories, we show that in both cases the connection can be decomposed as the sum of a Levi-Civita connection and terms depending on a vector field. However, while in case (i) this vector field is related to the symmetric part of the connection, in (ii) it comes from the torsion part and, therefore, it vanishes once torsion is completely removed. Moreover, the vanishing of this torsion-related vector field immediately implies the vanishing of the antisymmetric part of the Ricci tensor, which therefore plays no role in the dynamics. Related to this, we find that the Levi-Civita part of the connection is due to the existence of an invariant volume associated with an auxiliary metric h(mu v), which is algebraically related with the physical metric g(mu v).
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Babichev, E., & Fabbri, A. (2014). Rotating black holes in massive gravity. Phys. Rev. D, 90(8), 084019–7pp.
Abstract: We present a solution for rotating black holes in massive gravity. We first give a solution of massive gravity with one dynamical metric. Both metrics of this solution are expressed in the advanced Eddington-Finkelstein-like coordinates: the physical metric has the original Kerr line element, while the fiducial metric is flat, but written in a rotating Eddington-Finkelstein form. For the bigravity theory we give an analogue of this solution: the two metrics have the original Kerr form, but, in general, different black hole masses. The generalization of the solution to include the electric charge is also given; it is an analogue of the Kerr-Newman solution in general relativity. We also discuss further possible ways to generalize the solutions.
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del Rio, A., Navarro-Salas, J., & Torrenti, F. (2014). Renormalized stress-energy tensor for spin-1/2 fields in expanding universes. Phys. Rev. D, 90(8), 084017–15pp.
Abstract: We provide an explicit expression for the renormalized expectation value of the stress-energy tensor of a spin-1/2 field in a spatially flat Friedmann-Lemaitre-Robertson-Walker universe. Its computation is based on the extension of the adiabatic regularization method to fermion fields introduced recently in the literature. The tensor is given in terms of UV-finite integrals in momentum space, which involve the mode functions that define the quantum state. As illustrative examples of the method efficiency, we see how to compute the renormalized energy density and pressure in two interesting cosmological scenarios: a de Sitter spacetime and a radiation-dominated universe. In the second case, we explicitly show that the late-time renormalized stress-energy tensor behaves as that of classical cold matter. We also check that, if we obtain the adiabatic expansion of the scalar field mode functions with a similar procedure to the one used for fermions, we recover the well-known WKB-type expansion.
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Harko, T., Koivisto, T. S., Lobo, F. S. N., & Olmo, G. J. (2012). Metric-Palatini gravity unifying local constraints and late-time cosmic acceleration. Phys. Rev. D, 85(8), 084016–5pp.
Abstract: We present a novel approach to modified theories of gravity which consists of adding to the Einstein-Hilbert Lagrangian an f(R) term constructed a la Palatini. Using the respective dynamically equivalent scalar-tensor representation, we show that the theory can pass the Solar System observational constraints even if the scalar field is very light. This implies the existence of a long-range scalar field, which is able to modify the cosmological and galactic dynamics but leaves the Solar System unaffected. We also verify the absence of instabilities in perturbations and provide explicit models which are consistent with local tests and lead to the late-time cosmic acceleration.
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Barragan, C., & Olmo, G. J. (2010). Isotropic and anisotropic bouncing cosmologies in Palatini gravity. Phys. Rev. D, 82(8), 084015–15pp.
Abstract: We study isotropic and anisotropic (Bianchi I) cosmologies in Palatini f(R) and f(R, R μnu R μnu) theories of gravity with a perfect fluid and consider the existence of nonsingular bouncing solutions in the early universe. We find that all f(R) models with isotropic bouncing solutions develop shear singularities in the anisotropic case. On the contrary, the simple quadratic model R + aR(2)/R-P + R μnu R μnu/R-P exhibits regular bouncing solutions in both isotropic and anisotropic cases for a wide range of equations of state, including dust (for a<0) and radiation (for arbitrary a). It thus represents a purely gravitational solution to the big bang singularity and anisotropy problems of general relativity without the need for exotic (w>1) sources of matter/energy or extra degrees of freedom.
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Bernabeu, J., Espinoza, C., & Mavromatos, N. E. (2010). Cosmological constant and local gravity. Phys. Rev. D, 81(8), 084002–7pp.
Abstract: We discuss the linearization of Einstein equations in the presence of a cosmological constant, by expanding the solution for the metric around a flat Minkowski space-time. We demonstrate that one can find consistent solutions to the linearized set of equations for the metric perturbations, in the Lorentz gauge, which are not spherically symmetric, but they rather exhibit a cylindrical symmetry. We find that the components of the gravitational field satisfying the appropriate Poisson equations have the property of ensuring that a scalar potential can be constructed, in which both contributions, from ordinary matter and Lambda > 0, are attractive. In addition, there is a novel tensor potential, induced by the pressure density, in which the effect of the cosmological constant is repulsive. We also linearize the Schwarzschild-de Sitter exact solution of Einstein's equations ( due to a generalization of Birkhoff's theorem) in the domain between the two horizons. We manage to transform it first to a gauge in which the 3-space metric is conformally flat and, then, make an additional coordinate transformation leading to the Lorentz gauge conditions. We compare our non-spherically symmetric solution with the linearized Schwarzschild-de Sitter metric, when the latter is transformed to the Lorentz gauge, and we find agreement. The resulting metric, however, does not acquire a proper Newtonian form in terms of the unique scalar potential that solves the corresponding Poisson equation. Nevertheless, our solution is stable, in the sense that the physical energy density is positive.
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Wang, D., & Mena, O. (2024). Robust analysis of the growth of structure. Phys. Rev. D, 109(8), 083539–18pp.
Abstract: Current cosmological tensions show that it is crucial to test the predictions from the canonical ACDM paradigm at different cosmic times. One very appealing test of structure formation in the Universe is the growth rate of structure in our universe f, usually parametrized via the growth index gamma, with f equivalent to Omega(m)(a)gamma and gamma similar or equal to 0.55 in the standard ACDM case. Recent studies have claimed a suppression of the growth of structure from a variety of cosmological observations, characterized by gamma > 0.55. By employing different self-consistent growth parametrizations schemes, we show here that gamma < 0.55, obtaining instead an enhanced growth of structure today. This preference reaches the 3 sigma significance using cosmic microwave background observations, supernova Ia and baryon acoustic oscillation measurements. The addition of cosmic microwave background lensing data relaxes such a preference to the 2 sigma level, since a larger lensing effect can always be compensated with a smaller structure growth, or, equivalently, with gamma > 0.55. We have also included the lensing amplitude AL as a free parameter in our data analysis, showing that the preference for AL > 1 still remains, except for some particular parametrizations when lensing observations are included. We also do not find any significant preference for an oscillatory dependence of AL, AL + Am sin l. To further reassess the effects of a nonstandard growth, we have computed by means of N-body simulations the dark matter density fields, the dark matter halo mass functions and the halo density profiles for different values of gamma. Future observations from the Square Kilometer Array, reducing by a factor of 3 the current errors on the gamma parameter, further confirm or refute with a strong statistical significance the deviation of the growth index from its standard value.
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Barenboim, G., Kinney, W. H., & Morse, M. J. P. (2018). Phantom Dirac-Born-Infeld dark energy. Phys. Rev. D, 98(8), 083531–11pp.
Abstract: Motivated by the apparent discrepancy between cosmic microwave background measurements of the Hubble constant and measurements from Type-la supernovae, we construct a model for dark energy with equation of state w = p/rho < -1, violating the null energy condition. Naive canonical models of so-called “phantom” dark energy require a negative scalar kinetic term, resulting in a Hamiltonian unbounded from below and associated vacuum instability. We construct a scalar field model for dark energy with w < -1, which nonetheless has a Hamiltonian bounded from below in the comoving reference frame, i.e., in the rest frame of the fluid. We demonstrate that the solution is a cosmological attractor, and find that early-time cosmological boundary conditions consist of a “frozen” scalar field, which relaxes to the attractor solution once the dark energy component dominates the cosmological energy density. We consider the model in an arbitrary choice of gauge, and find that, unlike the case of comoving gauge, the fluid Hamiltonian is in fact unbounded from below in the reference frame of a highly boosted observer, corresponding to a nonlinear gradient instability. We discuss this in the context of general NEC-violating perfect fluids, for which this instability is a general property.
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Di Valentino, E., Giusarma, E., Mena, O., Melchiorri, A., & Silk, J. (2016). Cosmological limits on neutrino unknowns versus low redshift priors. Phys. Rev. D, 93(8), 083527–11pp.
Abstract: Recent cosmic microwave background (CMB) temperature and polarization anisotropy measurements from the Planck mission have significantly improved previous constraints on the neutrino masses as well as the bounds on extended models with massless or massive sterile neutrino states. However, due to parameter degeneracies, additional low redshift priors are mandatory in order to sharpen the CMB neutrino bounds. We explore here the role of different priors on low redshift quantities, such as the Hubble constant, the cluster mass bias, and the reionization optical depth tau. Concerning current priors on the Hubble constant and the cluster mass bias, the bounds on the neutrino parameters may differ appreciably depending on the choices adopted in the analyses. With regard to future improvements in the priors on the reionization optical depth, a value of tau = 0.05 +/- 0.01, motivated by astrophysical estimates of the reionization redshift, would lead to Sigma m(nu) < 0.0926 eV at 90% C.L., when combining the full Planck measurements, baryon acoustic oscillation, and Planck clusters data, thereby opening the window to unravel the neutrino mass hierarchy with existing cosmological probes.
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Di Valentino, E., Gariazzo, S., Gerbino, M., Giusarma, E., & Mena, O. (2016). Dark radiation and inflationary freedom after Planck 2015. Phys. Rev. D, 93(8), 083523–28pp.
Abstract: The simplest inflationary models predict a primordial power spectrum (PPS) of the curvature fluctuations that can be described by a power-law function that is nearly scale invariant. It has been shown, however, that the low-multipole spectrum of the cosmic microwave background anisotropies may hint at the presence of some features in the shape of the scalar PPS, which could deviate from its canonical power-law form. We study the possible degeneracies of this nonstandard PPS with the active neutrino masses, the effective number of relativistic species, and a sterile neutrino or a thermal axion mass. The limits on these additional parameters are less constraining in a model with a nonstandard PPS when including only the temperature autocorrelation spectrum measurements in the data analyses. The inclusion of the polarization spectra noticeably helps in reducing the degeneracies, leading to results that typically show no deviation from the Lambda CDM model with a standard power-law PPS. These findings are robust against changes in the function describing the noncanonical PPS. Albeit current cosmological measurements seem to prefer the simple power-law PPS description, the statistical significance to rule out other possible parametrizations is still very poor. Future cosmological measurements are crucial to improve the present PPS uncertainties.
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