Applications of Symmetry to the Large
Scale Structure of the Universe (Scale
Invariance) and to the Hadronic
Spectrum (Heavy Diquark Symmetry)
Mark B. Wise
Abstract Two applications of symmetries of quantum theories that are relevant in
very different circumstances, early universe cosmology and hadronic physics, are
discussed. The first concerns constraints on the form of correlations of the density
perturbations in the very early universe. The second is about the hadronic spectrum,
in particular states with flavor quantum numbers corresponding to two heavy bottom
quarks and two light anti-quarks (tetraquarks with two heavy quarks).
Keywords Symmetry · Scale invariance · Hadronic spectrum
1 Scale Invariance and Inflationary Cosmology
In this section I will not provide references to the early pioneering work on inflation.
They can be found in the excellent review [1].
The inflationary cosmology is a hypothetical era in the very early universe
when the energy density was dominated by potential energy (i.e., an effective
cosmological constant). We view this as arising from the evolution of a scalar field
(the inflation) which temporarily is moving slowly along a flat part of its potential
with almost constant energy density V . If there is a large enough smooth patch of
space time the metric in that patch becomes de Sitter space time, where
ds
2
= −dt
2
+ a(t)
2 dx
i dx
i , a(t) = e
H t and H
2
=
8π
3
GV .
(1)
With enough of this de Sitter exponential expansion this smooth patch can expand
to cover the whole visible universe. Eventually the scalar field enters a part of
its potential where it moves more rapidly towards the minimum and the universe
M. B. Wise ()
Walter Burke Institute for Theoretical Physics, California Institute of Technology,
Pasadena, CA, USA
e-mail: wise@theory.caltech.edu
© Springer Nature Switzerland AG 2021
M. B. Paranjape et al. (eds.), Quantum Theory and Symmetries, CRM Series in
Mathematical Physics, https://doi.org/10.1007/978-3-030-55777-5_51
545
Scale Structure of the Universe (Scale
Invariance) and to the Hadronic
Spectrum (Heavy Diquark Symmetry)
Mark B. Wise
Abstract Two applications of symmetries of quantum theories that are relevant in
very different circumstances, early universe cosmology and hadronic physics, are
discussed. The first concerns constraints on the form of correlations of the density
perturbations in the very early universe. The second is about the hadronic spectrum,
in particular states with flavor quantum numbers corresponding to two heavy bottom
quarks and two light anti-quarks (tetraquarks with two heavy quarks).
Keywords Symmetry · Scale invariance · Hadronic spectrum
1 Scale Invariance and Inflationary Cosmology
In this section I will not provide references to the early pioneering work on inflation.
They can be found in the excellent review [1].
The inflationary cosmology is a hypothetical era in the very early universe
when the energy density was dominated by potential energy (i.e., an effective
cosmological constant). We view this as arising from the evolution of a scalar field
(the inflation) which temporarily is moving slowly along a flat part of its potential
with almost constant energy density V . If there is a large enough smooth patch of
space time the metric in that patch becomes de Sitter space time, where
ds
2
= −dt
2
+ a(t)
2 dx
i dx
i , a(t) = e
H t and H
2
=
8π
3
GV .
(1)
With enough of this de Sitter exponential expansion this smooth patch can expand
to cover the whole visible universe. Eventually the scalar field enters a part of
its potential where it moves more rapidly towards the minimum and the universe
M. B. Wise ()
Walter Burke Institute for Theoretical Physics, California Institute of Technology,
Pasadena, CA, USA
e-mail: wise@theory.caltech.edu
© Springer Nature Switzerland AG 2021
M. B. Paranjape et al. (eds.), Quantum Theory and Symmetries, CRM Series in
Mathematical Physics, https://doi.org/10.1007/978-3-030-55777-5_51
545