Accuracy of the growth index in the presence of dark energy perturbations

We present the analytical solutions for the evolution of matter density perturbations, for a model with a constant dark energy equation of state $w$ but when the effects of the dark energy perturbations are properly taken into account. We consider two cases, the first when the sound speed of the perturbations is zero $c_s^2=0$ and the general case $0<c_s^2 \leq 1$. In the first case our solution is exact, while in the second case we found an approximate solution which works to better than $0.3\%$ accuracy for $k>10 H_0$ or equivalently $k/h>0.0033 \textrm{Mpc}^{-1}$. We also estimate the corrections to the growth index $\gamma(z)$, commonly used to parametrize the growth-rate. We find that these corrections due to the DE perturbations affect the growth index $\gamma$ at the $3\%$ level. We also compare our new expressions for the growth index with other expressions already present in the literature and we find that the latter are less accurate than the ones we propose here. Therefore, our analytical calculations are necessary as the theoretical predictions for the fundamental parameters to be constrained by the upcoming surveys need to be as accurate as possible, especially since we are entering in the precise cosmology era where parameters will be measured to the percent level.Comment: 8 pages, 4 figure

Gravitational wave energy emission and detection rates of Primordial Black Hole hyperbolic encounters

We describe in detail gravitational wave bursts from Primordial Black Hole (PBH) hyperbolic encounters. The bursts are one-time events, with the bulk of the released energy happening during the closest approach, which can be emitted in frequencies that could be within the range of both LIGO (10-1000Hz) and LISA ($10^{-6}-1$ Hz). Furthermore, we correct the results for the power spectrum of hyperbolic encounters found in the literature and present new exact and approximate expressions for the peak frequency of the emission. Note that these GW bursts from hyperbolic encounters between PBH are complementary to the GW emission from the bounded orbits of BHB mergers detected by LIGO, and help breaking degeneracies in the determination of the PBH mass, spin and spatial distributions.Comment: 12 pages, 8 figures. Changes match published versio

Gravitational wave bursts from Primordial Black Hole hyperbolic encounters

We propose that Gravitational Wave (GW) bursts with millisecond durations can be explained by the GW emission from the hyperbolic encounters of Primordial Black Holes in dense clusters. These bursts are single events, with the bulk of the released energy happening during the closest approach, and emitted in frequencies within the AdvLIGO sensitivity range. We provide expressions for the shape of the GW emission in terms of the peak frequency and amplitude, and estimate the rates of these events for a variety of mass and velocity configurations. We study the regions of parameter space that will allow detection by both AdvLIGO and, in the future, LISA. We find for realistic configurations, with total mass $M\sim60\,M_\odot$, relative velocities $v\sim 0.01\,c$, and impact parameters $b\sim10^{-3}$ AU, for AdvLIGO an expected event rate is ${\cal O}(10)$ events/yr/Gpc$^3$ with millisecond durations. For LISA, the typical duration is in the range of minutes to hours and the event-rate is ${\cal O}(10^3)$ events/yr/Gpc$^3$ for both $10^3\,M_\odot$ IMBH and $10^6\,M_\odot$ SMBH encounters. We also study the distribution functions of eccentricities, peak frequencies and characteristic timescales that can be expected for a population of scattering PBH with a log-normal distribution in masses, different relative velocities and a flat prior on the impact parameter.Comment: 5 pages, 6 figures, changes match published versio

Comparative analysis of model-independent methods for exploring the nature of dark energy

We make a comparative analysis of the various independent methods proposed in the literature for studying the nature of dark energy, using four different mocks of SnIa data. In particular, we explore a generic principal components analysis approach, the genetic algorithms, a series of approximations like Pad\'e power law approximants, and various expansions in orthogonal polynomials, as well as cosmography, and compare them with the usual fit to a model with a constant dark energy equation of state w. We find that, depending on the mock data, some methods are more efficient than others at distinguishing the underlying model, although there is no universally better method.Comment: 39 pages, 24 figures, changes match published versio

The Effective Fluid approach for Modified Gravity and its applications

In this review we briefly summarize the so-called effective fluid approach, which is a compact framework that can be used to describe a plethora of different modified gravity models as general relativity (GR) and a dark energy (DE) fluid. This approach, which is complementary to the cosmological effective field theory, has several benefits as it allows for the easier inclusion of most modified gravity models into the state-of-the-art Boltzmann codes, that are typically hard-coded for GR and DE. Furthermore, it can also provide theoretical insights into their behavior, since in linear perturbation theory it is easy to derive physically motivated quantities such as the DE anisotropic stress or the DE sound speed. We also present some explicit applications of the effective fluid approach with $f(R)$, Horndeski and Scalar-Vector-Tensor models, namely how this approach can be used to easily solve the perturbation equations and incorporate the aforementioned modified gravity models into Boltzmann codes so as to obtain cosmological constraints using Monte Carlo analyses.Comment: 25 pages, 4 figures. Invited review for the special issue on "Modified Gravity Approaches to the Tensions of LCDM", based on 1811.02469, 1904.06294 and 2206.0289