Editing Negative mass (section)

==Arrow of time and energy inversion==

In [[general relativity]], the universe is described as a [[Riemannian manifold]] associated to a [[metric tensor]] solution of Einstein's field equations. In such a framework, the runaway motion forbids the existence of negative matter.<ref name="Bondi 1957" /><ref name="Bonnor 1989" />

Some [[bimetric theory|bimetric theories]] of the universe propose that two [[multiverse|parallel universes]] with an opposite arrow of time may exist instead of one, linked together by the [[Big Bang]] and interacting only through [[gravitation]].<ref name="Sakharov 1980">{{cite journal |first=A.D. |last=Sakharov |title=&nbsp; |trans-title=Cosmological model of the Universe with a time vector inversion |journal=ZhETF |volume=79 |pages=689–693 |year=1980 |language=ru}}{{full citation needed|reason=original Russian title, full name of journal, DOI or link URL|date=January 2020}} <br/>translation in {{cite journal |title=Cosmological model of the Universe with a time vector inversion |journal=JETP Lett. |volume=52 |pages=349–351 |year=1980 |language=en}}{{full citation needed|reason=translator name, full name of journal, DOI or link URL|date=January 2020}}
</ref><ref name="Barbour 2014">{{cite journal|last1=Barbour|first1=Julian|author-link=Julian Barbour|last2=Koslowski|first2=Tim|last3=Mercati|first3=Flavio|year=2014|title=Identification of a Gravitational Arrow of Time|journal=Physical Review Letters|volume=113|issue=18|pages=181101|arxiv=1409.0917|bibcode=2014PhRvL.113r1101B|doi=10.1103/PhysRevLett.113.181101|pmid=25396357|s2cid=25038135}}</ref> The universe is then described as a manifold associated to two Riemannian metrics (one with positive mass matter and the other with negative mass matter). According to group theory, the matter of the [[Topological conjugacy|conjugated]] metric would appear to the matter of the other metric as having opposite mass and arrow of time (though its [[proper time]] would remain positive). The coupled metrics have their own [[geodesic]]s and are solutions of two coupled field equations.<ref name="Hossenfelder 2008">{{cite journal|last1=Hossenfelder|first1=S.|author-link=Sabine Hossenfelder|date=15 August 2008|title=A Bi-Metric Theory with Exchange Symmetry|journal=Physical Review D|volume=78|issue=4|page=044015|arxiv=0807.2838|bibcode=2008PhRvD..78d4015H|doi=10.1103/PhysRevD.78.044015|s2cid=119152509}}</ref>

The negative matter of the coupled metric, interacting with the matter of the other metric via gravity, could be an alternative candidate for the explanation of [[dark matter]], [[dark energy]], [[Inflation (cosmology)|cosmic inflation]] and an [[accelerating universe]].<ref name="Hossenfelder 2008"/>