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Register a new userCosmography with the Einstein Telescope
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Added by
B. S. Sathyaprakash
Publication date
2009
fields
Physics
and research's language is
English
Authors
B.S. Sathyaprakash
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Einstein Telescope (ET) is a 3rd generation gravitational-wave (GW) detector that is currently undergoing a design study. ET can detect millions of compact binary mergers up to redshifts 2-8. A small fraction of mergers might be observed in coincidence as gamma-ray bursts, helping to measure both the luminosity distance and red-shift to the source. By fitting these measured values to a cosmological model, it should be possible to accurately infer the dark energy equation-of-state, dark matter and dark energy density parameters. ET could, therefore, herald a new era in cosmology.
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A method to set constraints on the parameters of extended theories of gravitation is presented. It is based on the comparison of two series expansions of any observable that depends on H(z). The first expansion is of the cosmographical type, while the second uses the dependence of H with z furnished by a given type of extended theory. When applied to f(R) theories together with the redshift drift, the method yields limits on the parameters of two examples (the theory of Hu and Sawicki (2007), and the exponential gravity introduced by Linder (2009)) that are compatible with or more stringent than the existing ones, as well as a limit for a previously unconstrained parameter.
In this paper we analyze the implications of gravitational waves (GWs) as standard sirens on the modified gravity models by using the third-generation gravitational wave detector, i.e., the Einstein Telescope. Two viable models in $f(R)$ theories within the Palatini formalism are considered in our analysis ($f_{1}(mathcal{R})=mathcal{R}-frac{beta}{mathcal{R}^{n}}$ and $f_{2}(mathcal{R})=mathcal{R}+alphaln{mathcal{R}}-beta$), with the combination of simulated GW data and the latest electromagnetic (EM) observational data (including the recently released Pantheon type Ia supernovae sample, the cosmic chronometer data, and baryon acoustic oscillation distance measurements). Our analysis reveals that the standard sirens GWs, which provide an independent and complementary alternative to current experiments, could effectively eliminate the degeneracies among parameters in the two modified gravity models. In addition, we thoroughly investigate the nature of geometrical dark energy in the modified gravity theories with the assistance of $Om(z)$ and statefinder diagnostic analysis. The present analysis makes it clear-cut that the simplest cosmological constant model is still the most preferred by the current data. However, the combination of future naturally improved GW data most recent EM observations will reveal the consistency or acknowledge the tension between the $Lambda$CDM model and modified gravity theories.
In this work, we use the simulated gravitational wave (GW) standard siren data from the future observation of the Einstein Telescope (ET) to constrain various dark energy cosmological models, including the $Lambda$CDM, $w$CDM, CPL, $alpha$DE, GCG, and NGCG models. We also use the current mainstream cosmological electromagnetic observations, i.e., the cosmic microwave background anisotropies data, the baryon acoustic oscillations data, and the type Ia supernovae data, to constrain these models. We find that the GW standard siren data could tremendously improve the constraints on the cosmological parameters for all these dark energy models. For all the cases, the GW standard siren data can be used to break the parameter degeneracies generated by the current cosmological electromagnetic observational data. Therefore, it is expected that the future GW standard siren observation from the ET would play a crucial role in the cosmological parameter estimation in the future. The conclusion of this work is quite solid because it is based on the analysis for various dark energy models.
Cosmography is a powerful tool to investigate the Universe kinematic and then to reconstruct dynamics in a model-independent way. However, recent new measurements of supernovae Ia and quasars have populated the Hubble diagram up to high redshifts ($z sim 7.5$) and the application of the traditional cosmographic approach has become less straightforward due to the large redshifts implied. Here we investigate this issue through an expansion of the luminosity distance-redshift relation in terms of orthogonal logarithmic polynomials. In particular we point out the advantages of a new procedure of orthogonalization and we show that such an expansion provides a very good fit in the whole $z=0div 7.5$ range to both real and mock data obtained assuming various cosmological models. Moreover, despite of the fact that the cosmographic series is tested well beyond its convergence radius, the parameters obtained expanding the luminosity distance - redshift relation for the $Lambda$CDM model are broadly consistent with the results from a fit of mock data obtained with the same cosmological model. This provides a method to test the reliability of a cosmographic function to study cosmological models at high redshifts and it demonstrates that the logarithmic polynomial series can be used to test the consistency of the $Lambda$CDM model with the current Hubble diagram of quasars and supernovae Ia. We confirm a strong tension (at $>4sigma$) between the concordance cosmological model and the Hubble diagram at $z>1.5$. Such a tension is dominated by the contribution of quasars at $z>2$ and starts to be present also in the few supernovae Ia observed at $z>1$.
We study the holographic dark energy (HDE) model by using the future gravitational wave (GW) standard siren data observed from the Einstein Telescope (ET) in this work. We simulate 1000 GW standard siren data based on a 10-year observation of the ET to make this analysis. We find that all the cosmological parameters in the HDE model can be tremendously improved by including the GW standard siren data in the cosmological fit. The GW data combined with the current cosmic microwave background anisotropies, baryon acoustic oscillations, and type Ia supernovae data will measure the cosmological parameters $Omega_{rm m}$, $H_0$, and $c$ in the HDE model to be at the accuracies of 1.28%, 0.59%, and 3.69%, respectively. A comparison with the cosmological constant model and the constant-$w$ dark energy model shows that, compared to the standard model, the parameter degeneracies will be broken more thoroughly in a dynamical dark energy model. We find that the GW data alone can provide a fairly good measurement for $H_0$, but for other cosmological parameters the GW data alone can only provide rather weak measurements. However, due to the fact that the parameter degeneracies can be broken by the GW data, the standard sirens can play an essential role in improving the parameter estimation.
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