Horndessence: $Lambda$CDM Cosmology from Modified Gravity. (arXiv:2104.14560v1 [gr-qc])

<a href="http://arxiv.org/find/gr-qc/1/au:+Linder_E/0/1/0/all/0/1">Eric V. Linder</a>

Rather than obtaining cosmic acceleration with a scalar field potential

(quintessence) or noncanonical kinetic term (k-essence), we can do it purely

through a modified gravity braiding of the scalar and metric, i.e. the $G_3$

Horndeski action term. Such “Horndessence” allows an exact $Lambda$CDM

cosmological expansion without any cosmological constant, and by requiring

shift symmetry we can derive the exact form of $G_3$. We find that this route

of deriving $G_3(X)$ leads to a functional form far from the usual simple

assumptions such as a power law. Horndessence without any kinetic term or

potential has the same number of parameters as $Lambda$CDM and makes an exact

prediction for the expansion history ($Lambda$CDM) and modified gravity cosmic

growth history; we show the viable gravitational strength $G_{rm eff}(a)$ and

growth rate $fsigma_8(a)$. The simplest versions of the theory fail soundness

criteria, but we learn interesting lessons along the way, in particular about

robust parametrization, and indicate possible sound extensions.

Rather than obtaining cosmic acceleration with a scalar field potential

(quintessence) or noncanonical kinetic term (k-essence), we can do it purely

through a modified gravity braiding of the scalar and metric, i.e. the $G_3$

Horndeski action term. Such “Horndessence” allows an exact $Lambda$CDM

cosmological expansion without any cosmological constant, and by requiring

shift symmetry we can derive the exact form of $G_3$. We find that this route

of deriving $G_3(X)$ leads to a functional form far from the usual simple

assumptions such as a power law. Horndessence without any kinetic term or

potential has the same number of parameters as $Lambda$CDM and makes an exact

prediction for the expansion history ($Lambda$CDM) and modified gravity cosmic

growth history; we show the viable gravitational strength $G_{rm eff}(a)$ and

growth rate $fsigma_8(a)$. The simplest versions of the theory fail soundness

criteria, but we learn interesting lessons along the way, in particular about

robust parametrization, and indicate possible sound extensions.

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