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The memory of primordial gravitational waves

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International Journal of Modern Physics A
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Paolo Creminelli
Paolo Creminelli
Paolo Creminelli
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Filippo Vernizzi
Filippo Vernizzi
Filippo Vernizzi
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Abstract and Figures

Primordial gravitational waves, after they enter the horizon and decay away, leave a residual displacement in test particles: a memory, in analogy with gravitational waves generated by astrophysical sources. The late-time distance between test particles is related to the one at early times by ξlatei=alateaearly(δji−12h̄ji)ξearlyj. Therefore, the deformation of an initial spherical shell does not depend on the cosmological evolution, but only on the primordial value h̄ji of the gravitational wave. The memory is thus related to the adiabatic tensor mode that maps the unperturbed FLRW geometries at early and late times; this is analogous to the relation between memory in Minkowski spacetime and the BMS group. The primordial memory is also connected to the consistency relations of cosmological correlators, as the flat-space memory is related to the soft theorems for gravitational wave emission. We comment on the signature of the effect on the CMB B-modes and on the large-scale structure. There is also a primordial memory effect that is subleading in the spatial gradients of the wave: it is encoded in the rotation of free-falling gyroscopes. To the memory of Valery A. Rubakov. Contribution to the special issue of the International Journal of Modern Physics A.
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The memory of primordial gravitational waves
Paolo Creminelli
*,†,§
and Filippo Vernizzi
‡,
*
International Centre for Theoretical Physics,
Strada Costiera 11, 34151 Trieste, Italy
†
Institute for Fundamental Physics of the Universe,
Via Beirut 2, 34014 Trieste, Italy
‡
Institut de Physique Theorique,
Universit
eParis Saclay,
CEA, CNRS, 91191 Gif-sur-Yvette, France
§
creminel@ictp.it
filippo.vernizzi@ipht.fr
Received 27 July 2024
Revised 3 December 2024
Accepted 6 December 2024
Published 17 March 2025
Primordial gravitational waves, after they enter the horizon and decay away, leave a residual
displacement in test particles: a memory, in analogy with gravitational waves generated by
astrophysical sources. The late-time distance between test particles is related to the one at early
times by i
late ¼alate
aearly ði
j1
2
hi
jÞj
early. Therefore, the deformation of an initial spherical shell does
not depend on the cosmological evolution, but only on the primordial value
hi
jof the gravitational
wave. The memory is thus related to the adiabatic tensor mode that maps the unperturbed FLRW
geometries at early and late times; this is analogous to the relation between memory in Minkowski
spacetime and the BMS group. The primordial memory is also connected to the consistency
relations of cosmological correlators, as the °at-space memory is related to the soft theorems for
gravitational wave emission. We comment on the signature of the e®ect on the CMB B-modes and
on the large-scale structure. There is also a primordial memory e®ect that is subleading in the
spatial gradients of the wave: it is encoded in the rotation of free-falling gyroscopes.
To the memory of Valery A. Rubakov. Contribution to the special issue of the International
Journal of Modern Physics A.
Keywords: In°ation; early universe; gravitational waves.
PACS numbers: 04.30.-w, 98.80.Cq
The memory e®ect of gravitational waves (GWs) is the residual displacement of test
particles after the passage of the wave. GWs emitted by astrophysical sources give a
§
Corresponding author.
International Journal of Modern Physics A
(2025) 2540001 (10 pages)
#
.
cWorld Scienti¯c Publishing Company
DOI: 10.1142/S0217751X25400019
2540001-1
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