Cosmological implications of quantum entanglement in the multiverse

Cosmological implications of quantum entanglement in the multiverse Sugumi Kanno (University of the Basque Country) based on ar. Xiv: 1404. 6815 [hep-th]; JHEP 1407 (2014) 072 ar. Xiv: 1405. 7793 [hep-th]; JCAP 1407 (2014) 029 ar. Xiv: 1506. 07808 [hep-th]; PLB 751 (2015) 316

Inflationary cosmology/String landscape suggest that our universe may not be the only universe but is part of a vast complex of universes that we call the multiverse. Our universe Space between universes expands some other universe out there © National Geographic Is our we is entangled detect observable with the signatures? universe out there? Canuniverse we. Can confirm the existence of other universes? 1

Quantum entanglement? The most fascinating aspect: Einstein-Podolsky-Rosen paradox To affect the outcome of local measurements instantaneously once a local measurement is performed. The information travels faster than the speed of light? Eg) An entangled pair of electrons ups or downs? my friend The instant I measure But my it, Ifriend immediately doesn’tan know which until spin measures my friend it. out there Quantum entanglement is purely aspect of he quantum physics that is sowill find. different from classical physics. Causality remains intact. 2

Entanglement exists in arbitrary large distances In principle, you gain information about the partner particle by measuring your own particle wherever the partner particle goes, if they are entangled. Who takes the partner particle to a causally disconnected region? the moon a different galaxy a causally disconnected different universe 3

Inflationary universe can do it Inflationary universe is approximated by a de Sitter space Vacuum state is full of virtual particles in pairs Quantum fluctuations out there Quantum fluctuations time entanglement couldmay exist a with Quantum fluctuations in our universe bebeyond entangled cosmological horizon those in the universe out there(the Hubble horizon). A pair of particles created within a causally connected cosmological horizon size region 4

Inflationary universe Inflationary is auniverse phenomenologically magnifies quantum very successful fluctuations ideato cosmic size. time de Sitter Quantum fluctuations Entangled with some other universe!? Afterwards In fact, might it has evolution been of ourof universe shown that could causally beout correlated disconnected There be arecently copy our universe there !? regions to the universe in de Sitter out space there!? are entangled. 5

Good news Maldacena & Pimentel (2013) Kanno, Murugan, Shock & Soda (2014) Two causally disconnected regions in de Sitter space have been shown to be entangled. Vacuum in our universe may Can we fluctuations observe theobserved effect of the entanglement be entangled with those in theregion? universe out there. with a causally disconnected Entanglement entropy We may make use of the cosmic microwave background to find a signature of entanglement with the universe out there. 6

The Cosmic Microwave Background (CMB) The CMB is thermal radiation and the oldest light in our universe. ed shift d or Blue e t if h s d e R Planck Redshifte d or Blue shift Quantum fluctuations of an inflaton field After inflation ed WMAP 400, 000 Years Spacetime flucuations Energy fluctuations of photons = anisotropies of the CMB 7

The cosmic microwave background (CMB) anisotropy A snapshot of the oldest epoch in our universe, when it was about 400, 000 years old. © ESA and the Planck collaboration Take the ensemble Blue average Red spots: in evolve each slightly scale: intohot, stars small Blue and scales spots: galaxies (many slightly afterwards data), coldlarge scales (a few) 8

Power spectrum of temperature fluctuations Standard inflationary model Measurement We hope to find some signatures of entanglement on small scales Large scales Small scales © ESA and the Planck collaboration Entanglement affects. There the shape of agrees the spectrum onmeasurements large scales : Kanno (2014) Standard inflationary model very well are many data with on small scales but it would be hard to test because of the short of data. 9

As a first step to find a signature of entanglement, We focus on the effect of entanglement on the spectrum of vacuum fluctuations of an inflaton field during inflation. Planck WMAP Quantum fluctuations of an inflaton field 400, 000 Years Spacetime flucuations Energy fluctuations of photons 10

String/cosmic landscape Sato et al. (1981), Vilenkin (1983), Linde (1986), Bousso & Polchinski (2000), Susskind (2003) The configuration space of all possible values of scalar fields with all possible potentials. There about 10 500 vacua in string landscape Quantum tunneling takes place in many places This tunneling process produces the multiverse ling e nn Tu g lin e nn Tu 11

Multiverse: String/cosmic landscape Eg) One type of potential of a scalar field in the landscape Eternal inflation Tun n time eling de Sitter multiverse Causal diagram of the inflationary multiverse 12

Our universe may be nucleated initially as an entangled state with another universe !? 13

Entangled states Eg) An entangled pair of electrons If our universe (BD 1) was nucleated as an entangled state with another universe (BD 2), The degree of entanglement Vacuum state Single particle excited state of a scalar field BD 1 The degree of entanglement holds the conservation of probability : Maximally entangled state In general, the degree of entanglement is complex and depends on scales 14

A pair of entangled universes Initially entangled state BD 1 BD 2 Ex p sp of n sp a io of time ce ns n Ex pa sio ac e an Initially entangled state de Sitter multiverse Causal diagram of the inflationary multiverse 15

Spectrum of vacuum fluctuations on small scales Kanno (2015) Maximally entangled case This In order enhancement to clearly is see due thetoeffect the single of entanglement, particle excited let’sstate examine in our a non-entangled simple model, state and not thatdue includes to thesingle effectparticle of entanglement. excited states. Standard inflationary universe 16

Non-entangled states Eg) An non-entangled pair of electrons (direct product form) If our universe was nucleated in a non-entangled state with the other universe Conservation Non-entangled of state probability has two holds extra in combinations each BD 1 and (off-diagonal BD 2 elements) The off-diagonal elements represent quantum interference 17

Quantum interference This quantum nature contributes to the spectrum as oscillatory modulations on small scales if our universe was initially non-entangled with another universe. © Akira Tonomura 18

Spectrum of vacuum fluctuations In the case of standard inflationary universe : flat spectrum : Hubble parameter In the case of initially general entangled state In the case of initially maximally entangled state Since the scale dependence is purely an aspect of entanglement, the effect of entanglement may be imprinted on the spectrum Remember : the degree of entanglement : enhanced flat spectrum : enhanced scale dependent spectra has as enhanced scale dependent behaviors. scale dependence in general due to the single particle excitated state In the case of initially non-entangled state : oscillatory spectra due to the quantum interference : parameter 19

Non-entangled state: Oscillatory spectra (artificial) If we consider the afterwards evolution of our universe and expand the temperature fluctuations in spherical harmonics we would be able to obtain… Standard inflationary universe If we consider moreof concrete inflationismodels, we would be able cannot to predict If the amplitude the oscillation very small, the spectrum 20 more oscillatory beconcrete distinguished from aspectra. flat spectrum.

Power spectrum of temperature fluctuations Standard inflationary model Measurement If we analyze various other observables such as the bi-spectrum, tri-spectrum etc, we may be able to distinguish the effect of entanglement in the future. © ESA and the Planck collaboration But precision of Planck’s map is high enough already, webe may not be ablethat to see the If we found an oscillatory modulation, it may a signature modulation in the spectrum. our universe was nucleated as a non-entangled state. 21

Summary If our universe was nucleated as an entangled state with another universe initially, the effect of entanglement may be imprinted on the cosmological observables. In our simple model, however, the effect was only to increase the amplitude of the spectrum. In order to make more concrete predictions, we need to consider more concrete inflation models and evolution of them. It will be also necessary to study the effect of entanglement on various other observables including the bi-spectrum, tri-spectrum, etc. These give rise to the possibility that the existence of multiverse may be experimentally tested in the near future. 22