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Gravity in the Era of Equality: Towards solutions to the Hubble problem without fine-tuned initial conditions
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abstract
Discrepant measurements of the Universe's expansion rate ($H_0$) may signal physics beyond the standard cosmological model. Here I describe two early modified gravity mechanisms that reconcile the value of $H_0$ by increasing the expansion rate in the era of matter-radiation equality. These mechanisms, based on viable Horndeski theories, require significantly less fine-tuned initial conditions than early dark energy with oscillating scalar fields. In Imperfect Dark Energy at Equality (IDEE), the initial energy density dilutes slower than radiation but faster than matter, naturally peaking around the era of equality. The minimal IDEE model, a cubic Galileon, is too constrained by the cosmic microwave background (Planck) and baryon acoustic oscillations (BAO) to relieve the $H_0$ tension. In Enhanced Early Gravity (EEG), the scalar field value modulates the cosmological strength of gravity. The minimal EEG model, an exponentially coupled cubic Galileon, gives a Planck+BAO value $H_0=68.7 \pm 1.5$ (68\% c.l.), reducing the tension with SH0ES from $4.4\sigma$ to $2.6\sigma$. Additionally, Galileon contributions to cosmic acceleration may reconcile $H_0$ via Late-Universe Phantom Expansion (LUPE). Combining LUPE, EEG and $\Lambda$ reduces the tension between Planck, BAO and SH0ES to $2.5\sigma$. I will also describe additional tests of coupled Galileons based on local gravity tests, primordial element abundances and gravitational waves. While further model building is required to fully resolve the $H_0$ problem and satisfy all available observations, these examples show the wealth of possibilities to solve cosmological tensions beyond Einstein's General Relativity.
Forward citations
Cited by 7 Pith papers
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Hubble tension: the shape wall
Late-time modifications to the expansion history can raise H0 by at most about 2% (conservative) to 3.7% (permissive) if the CMB acoustic scale is fixed.
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The $H_0$ world cup. II. A comprehensive competition between proposed Hubble tension solutions
Against a common 2025-26 dataset (Planck PR4, ACT DR6, SPT-3G, DESI DR2, Pantheon+), early dark energy and early modified gravity models win the H0 competition (~3σ residual tension), while radiation and late-time sol...
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Scalar-Tensor Gravity and DESI 2024 BAO data
With Planck and DESI BAO data, the Brans-Dicke Galileon model prefers a nonzero Galileon term and yields H0 = 71.0 +1.5 -1.3 km/s/Mpc, consistent with SH0ES at 1.2 sigma.
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The $H_0$ World Cup. I. Summary of the baseline group stage results
In a systematic head-to-head analysis, early dark energy and early modified gravity models reduce the Hubble tension to about 3σ and are favored over ΛCDM, while radiation and late-time alternatives are not.
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Reconstructions of Horndeski Subclasses by Gaussian Processes
The GP reconstructions favor a Brans-Dicke cosmology over ΛCDM at z≈0.4–1.7 and a Cubic Galileon with redshift-dependent dark-energy density across the full observed range.
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Imprint of swampland-inspired coupled early dark energy
A swampland-inspired DM-EDE coupling is tested against DESI DR2 BAO data, showing the EDE potential construction affects late-time dark energy constraints.
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Alleviating the $H_0$ tension through the interacting dark energy model from quantum gravitational field theory in light of DESI DR2
With DESI DR2 BAO plus CMB and a SH0ES prior, the two-parameter eeΛCDM model gives δΛ=-0.41±0.14 and H0=71.9±1.0, easing the Hubble tension to 0.8σ, but SN datasets erase the signal.
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