A Falsifiable Alternative to General Relativity

TL;DR

The paper introduces asymptotically Weyl-invariant gravity (AWIG) in the Palatini formalism, proposing a running exponent $n(\mathcal{R})$ that enforces UV Weyl invariance and recovers GR in the IR. By fixing the spacetime dimension and constructing a tractable $n(\mathcal{R}_{*})$ (e.g., $n(\mathcal{R}_{*})=1+3\mathcal{R}_{*}^{2}-2\mathcal{R}_{*}^{3}$) with a derived $\epsilon(\mathcal{R}_{*})$, the model yields a differential relation $T(\mathcal{R})$ that avoids common Palatini pathologies while remaining cosmologically viable. The theory makes a falsifiable prediction for the frequency evolution in binary black hole mergers: the observed frequency should differ from GR by a factor up to $\sqrt{2}$, corresponding to $f'(\mathcal{R})$ in $[0.58,2]$, giving testable deviations in gravitational waves. An analysis of GW150914 and GW151226 indicates small to moderate tensions with GR and a tendency toward AWIG across detectors and events, suggesting AWIG could capture real strong-field modifications; nonetheless, more data and rigorous renormalizability and unitarity studies are required to establish its viability.

Abstract

Asymptotically Weyl-invariant gravity (AWIG) is further developed within the Palatini formalism as a power-counting renormalizable alternative to general relativity (GR). An expression for the dimensionless exponent n(R) is derived based on dynamical dimensional reduction. We show that this version of AWIG naturally resolves several theoretical issues normally associated with the Palatini formalism. A falsifiable prediction regarding the frequency of gravitational waves from binary black hole mergers is made. A preliminary analysis of gravitational wave GW150914 yields a maximum tension of 0.9σ with GR and marginally favours AWIG. A similar analysis of gravitational wave GW151226 yields a maximum tension of 2.7σ with GR and favours AWIG more significantly.

Figures (11)

• Figure 1: (a) The dimensionless exponent $n\left(\mathcal{R}_{*}\right)$, (b) the Lagrangian density $f\left(\mathcal{R}_{*}\right)$, (c) its first derivative $f'\left(\mathcal{R}_{*}\right)$ and (d) the traced stress-energy tensor $T\left(\mathcal{R}_{*}\right)$. The upper (lower) dashed line in (a) gives the asymptotic value in the high-curvature (low-curvature) limit. The dashed line in (d) indicates the general relativistic dependency $T\left(\mathcal{R}_{*}\right)\propto -\mathcal{R}_{*}$.
• Figure 2: (a) Strain versus time and (b) frequency versus time from a numerical relativity simulation of GW150914 including a band-pass filter LIGOScientific:2016aoc. Error bands in (b) represent one standard deviation taken over three adjacent $\omega(t)$ values.
• Figure 3: (a) Frequency versus time for the gravitational-wave event GW150914 observed by LIGO Hanford. (b) An example pixel cross-section at $t=0.425$, where the dashed vertical lines show the peak intensity and the FWHM.
• Figure 4: The ratio $\omega_{GR}/\omega_{Han}$ as a function of time including error bands. The dashed horizontal line indicates the general relativistic prediction and the dashed vertical line indicates the approximate boundary between the inspiral and merge phases LIGOScientific:2016aoc. The upper shaded region indicates the AWIG prediction $(\omega_{GR}/ \omega_{AWIG})_{max}$ and the lower shaded region indicates the AWIG prediction $(\omega_{GR}/ \omega_{AWIG})_{min}$.
• Figure 5: (a) Strain versus time and (b) frequency versus time from a numerical relativity simulation of GW150914 projected on to L1 LIGOScientific:2016aoc. Error bands represent one standard deviation in the frequency taken over three adjacent $\omega(t)$ values.