Cosmological constraints on dark energy in light of gravitational wave bounds

Johannes Noller

Phys. Rev. D 101, 063524 – Published 20 March 2020

Abstract

Gravitational wave (GW) constraints have recently been used to significantly restrict models of dark energy and modified gravity. New bounds arising from GW decay and GW-induced dark energy instabilities are particularly powerful in this context, complementing bounds from the observed speed of GWs. We discuss the associated linear cosmology for Horndeski gravity models surviving these combined bounds and compute the corresponding cosmological parameter constraints, using cosmic microwave background, redshift space distortion, matter power spectrum, and baryon acoustic oscillation measurements from the Planck, Sloan Digital Sky Survey/Baryon Oscillation Spectroscopic Survey and 6dF surveys. The surviving theories are strongly constrained, tightening previous bounds on cosmological deviations from $Λ CDM$ by over an order of magnitude. We also comment on general cosmological stability constraints and the nature of screening for the surviving theories, pointing out that a raised strong coupling scale can ensure compatibility with gravitational wave constraints, while maintaining a functional Vainshtein screening mechanism on Solar System scales. Finally, we discuss the quasistatic limit as well as (constraints on) related observables for near-future surveys.

Received 29 January 2020
Accepted 27 February 2020

DOI:https://doi.org/10.1103/PhysRevD.101.063524

Physics Subject Headings (PhySH)

Alternative gravity theories Cosmological parameters Dark energy Gravitational waves

Large scale structure of the Universe

Gravitation, Cosmology & Astrophysics

Authors & Affiliations

Johannes Noller

Institute for Theoretical Studies, ETH Zürich, Clausiusstrasse 47, 8092 Zürich, Switzerland and Institute for Particle Physics and Astrophysics, ETH Zürich, 8093 Zürich, Switzerland

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Issue

Vol. 101, Iss. 6 — 15 March 2020

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Images

Figure 1
Cosmological parameter constraints for the dark energy $c_{B}$ and $c_{M}$ parameters, using the $α_{i} = c_{i} \cdot a$ (left triangle plot) and $α_{i} = c_{i} \cdot Ω_{DE}$ (right triangle plot) parametrizations and different combinations of datasets and priors (see Sec. 3). All constraints shown assume $α_{T} = 0$ , but note that constraints in the $c_{M} - c_{B}$ plane, as shown here, are only mildly affected by allowing $α_{T} \neq 0$ [39]. Contours mark 68% and 95% confidence intervals, computed using just Planck data (P15), Planck data plus RSD, BAO, and matter power spectrum measurements ( $P 15 + LSS$ ), and $P 15 + LSS$ with an additional prior ensuring the absence of GW-induced instabilities ( $P 15 + LSS + GW$ ). In Fig. 3, below we show that $P 15 + LSS + GW$ and $P 15 + GW$ lead to near identical constraints. Dotted lines mark $c_{i} = 0$ (the GR value), $c_{B} = 2$ (a singular line physical models cannot cross in the $α_{i} = c_{i} a$ parametrization—see [39, 65, 66] for details), and $c_{M} = - c_{B}$ (constraint derived from the GW prior).
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Figure 2
Illustration of the effect of varying $c_{M} = - c_{B}$ for the reduced Horndeski theory (8) consistent with the GW prior and when using the $α_{i} = c_{i} \cdot a$ parametrization, on the CMB TT power spectrum (left plot) and on $f σ_{8}$ (right plot). Data points are shown with $1 σ$ uncertainties and all standard $Λ CDM$ parameters are fixed to their Planck 2015 best-fit values here [67]. Increasing $c_{M} = - c_{B}$ for (8) very quickly adds too much power on large scales via the late Integrated Sachs Wolfe (ISW) effect. In fact, all $c_{M} \neq 0$ cosmologies shown here are ruled out at above $2 σ$ via this effect alone and only $c_{M} < 0.06$ is consistent at this level—c.f. Figs. 1 and 3. Planck data and the late ISW effect specifically therefore place the strongest bounds on (8). $f σ_{8}$ constraints from RSDs, on the other hand, have strong constraining power for general Horndeski models (where they rule out large $c_{M}$ cosmologies consistent with cosmic microwave background (CMB) measurements, as long as $c_{M}$ and $c_{B}$ are both $O (1)$ and positive), but only add very mild additional constraining power for the reduced Horndeski theory (8) (where $c_{B}$ is negative, whenever $c_{M}$ is positive).
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Figure 3
The 1D posterior distribution of $c_{M}$ , using the $α_{i} = c_{i} \cdot a$ (left plot) and $α_{i} = c_{i} \cdot Ω_{DE}$ (right plot) parametrizations and two different combinations of datasets and priors (see Sec. 3). We compare constraints derived for the reduced Horndeski theory (8) (i.e., when imposing the GW prior) using Planck data with vs without adding additional constraints from LSS measurements (as discussed in Sec. 3). We find that, for this set of theories, constraints obtained with and without adding the above LSS data are near identical.
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Figure 4
Plots of the ratio of $α_{M}$ and $(M^{2} - 1) / M^{2}$ vs redshift $z$ —cf. the terms in (b1) and (b2)—using the $α_{i} = c_{i} \cdot a$ (upper plot) and $α_{i} = c_{i} \cdot Ω_{DE}$ (lower plot) parametrizations. The ratio of these quantities during different eras is used to estimate quasistatic observables in Sec. 6. Values for $c_{i}$ are chosen to span the observationally allowed range of values–see Table 1. Faded vertical lines denote the redshifts of matter-dark energy and matter-radiation equality.
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