Can we detect quantum gravity with compact binary inspirals?

Abstract

Treating general relativity as an effective field theory, we compute the leading-order quantum corrections to the orbits and gravitational-wave emission of astrophysical compact binaries. These corrections are independent of the (unknown) nature of quantum gravity at high energies, and generate a phase shift and amplitude increase in the observed gravitational-wave signal. Unfortunately (but unsurprisingly), these corrections are undetectably small, even in the most optimistic observational scenarios. I. INTRODUCTIONGeneral relativity (GR) has passed an impressive range of observational tests in the weak-field (i.e., low-energy) regime [1]. However, it is well known that GR predicts the formation of singularities, indicating the breakdown of the theory in the extreme strong-field (high-energy) regime [2][3][4]. Resolving such singularities is a major motivation for the construction of a theory of quantum gravity (QG) [5], which is well-behaved at high energies but is equivalent to GR in the low-energy limit.The first attempts to quantise gravity failed due to the negative mass dimension of Newton's constant in 4D spacetime. In the perturbative approach, this creates infinitely many divergences, whose renormalisation introduces infinitely many undetermined couplings, causing a loss of predictivity of the theory [6][7][8][9][10].Despite this non-renormalisability, one can isolate the well-behaved low-energy regime of the theory from the divergences by integrating out the high-energy degrees of freedom [11][12][13]. This results in an effective field theory (EFT), which is a predictive, well-defined theory of QG at energies far below the Planck mass M P . (This is analogous to the standard model of particle physics, which has been verified to exquisite precision up to ∼ 10 −16 M P , but is expected to give way to new physics at higher energies.)Remarkably, the dominant corrections to GR in this EFT are parameter-free, and therefore independent of the high-energy completion of QG. One can thus calculate quantum corrections to low-energy gravitational phenomena, such as the Newtonian potential of two point masses [14,15] and the classical Schwarzschild and Kerr spacetimes [16]. These corrections are concrete, modelindependent predictions of QG. If observed, they would provide the first experimental evidence for the quantum nature of spacetime. 1

Quantum gravity and gravitational-wave astronomy

“…The chance is slim but it should be contrasted with the worse odds when considering only perturbative effects. For instance, in the effective field-theory approach to quantum gravity [122,123,179] high-energy modes are integrated out, the Newton potential receives corrections of the form (6.5) [120,121] and the emission of gravitational waves is affected [180,181], but these corrections are heavily suppressed. Similarly, perturbative modifications in dispersion relations are suppressed at least as K = k 2 (1 + Pl k) and they are virtually unconstrained in GW observations [118,119], as we also appreciated in our analysis.…”

Gravitational Waves: The Theorist’s Swiss Knife

“…Gravitational waves provide valuable information on astrophysical models of compact objects [6][7][8], the cosmic history of the universe [9,10], and the large-scale structure [11] independently of electromagnetic waves and corresponding observational tools like the cosmic microwave background. In addition, gravitational waves offer the means to test early universe processes [12][13][14], beyond the Standard Model particle physics at energy scales that cannot be reached by current or near-future particle accelerators [15,16], dark matter candidates [17][18][19][20][21], Einstein's theory of General Relativity [22,23], modified/extended gravity proposals [17,[24][25][26], and even quantum gravity candidate theories [27][28][29][30].…”

Gravitational Waves: the theorist's Swiss knife

“…Gravitational waves provide valuable information on astrophysical models of compact objects [6][7][8], the cosmic history of the universe [9,10], and the large-scale structure [11] independently of electromagnetic waves and corresponding observational tools like the cosmic microwave background. In addition, gravitational waves offer the means to test early universe processes [12][13][14], beyond the Standard Model particle physics at energy scales that cannot be reached by current or near-future particle accelerators [15,16], dark matter candidates [17][18][19][20][21], Einstein's theory of General Relativity [22,23], modified/extended gravity proposals [17,[24][25][26], and even quantum gravity candidate theories [27][28][29][30].…”