C-parity, magnetic monopoles, and higher frequency gravitational waves
Rinku Maji, Qaisar Shafi
Abstract
We consider the spontaneous breaking of <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"> <a:mi>S</a:mi> <a:mi>O</a:mi> <a:mo stretchy="false">(</a:mo> <a:mn>10</a:mn> <a:mo stretchy="false">)</a:mo> </a:math> grand unified symmetry to the left-right symmetric model <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"> <e:mi>S</e:mi> <e:mi>U</e:mi> <e:mo stretchy="false">(</e:mo> <e:mn>3</e:mn> <e:msub> <e:mo stretchy="false">)</e:mo> <e:mi>c</e:mi> </e:msub> <e:mo>×</e:mo> <e:mi>S</e:mi> <e:mi>U</e:mi> <e:mo stretchy="false">(</e:mo> <e:mn>3</e:mn> <e:msub> <e:mo stretchy="false">)</e:mo> <e:mi>L</e:mi> </e:msub> <e:mo>×</e:mo> <e:mi>S</e:mi> <e:mi>U</e:mi> <e:mo stretchy="false">(</e:mo> <e:mn>2</e:mn> <e:msub> <e:mo stretchy="false">)</e:mo> <e:mi>R</e:mi> </e:msub> <e:mo>×</e:mo> <e:mi>U</e:mi> <e:mo stretchy="false">(</e:mo> <e:mn>1</e:mn> <e:msub> <e:mo stretchy="false">)</e:mo> <e:mrow> <e:mi>B</e:mi> <e:mo>−</e:mo> <e:mi>L</e:mi> </e:mrow> </e:msub> </e:math> with C-parity also unbroken [ <o:math xmlns:o="http://www.w3.org/1998/Math/MathML" display="inline"> <o:mi>C</o:mi> </o:math> converts <q:math xmlns:q="http://www.w3.org/1998/Math/MathML" display="inline"> <q:mi>Q</q:mi> <q:mo stretchy="false">→</q:mo> <q:mo>−</q:mo> <q:mi>Q</q:mi> </q:math> , where <t:math xmlns:t="http://www.w3.org/1998/Math/MathML" display="inline"> <t:mi>Q</t:mi> </t:math> is the electric charge operator in <v:math xmlns:v="http://www.w3.org/1998/Math/MathML" display="inline"> <v:mi>S</v:mi> <v:mi>O</v:mi> <v:mo stretchy="false">(</v:mo> <v:mn>10</v:mn> <v:mo stretchy="false">)</v:mo> </v:math> .] This breaking produces the topologically stable grand unified theory (GUT) monopole as well as a GUT scale C-string. The subsequent breaking at an intermediate scale of C-parity produces domain walls bounded by C-strings, found by Kibble A limited number of inflationary <z:math xmlns:z="http://www.w3.org/1998/Math/MathML" display="inline"> <z:mi>e</z:mi> </z:math> -foldings experienced during these breakings can yield an observable number density of primordial GUT monopoles. The C-strings also experience this inflationary phase, and the subsequent string-wall network decays through the emission of gravitational waves. We estimate the gravitational wave spectrum from these composite structures over a range of values of the domain wall tension <bb:math xmlns:bb="http://www.w3.org/1998/Math/MathML" display="inline"> <bb:mi>σ</bb:mi> </bb:math> . Depending on <db:math xmlns:db="http://www.w3.org/1998/Math/MathML" display="inline"> <db:mi>σ</db:mi> </db:math> the spectrum displays a peak in the higher frequency range between <fb:math xmlns:fb="http://www.w3.org/1998/Math/MathML" display="inline"> <fb:msup> <fb:mn>10</fb:mn> <fb:mn>2</fb:mn> </fb:msup> </fb:math> and <hb:math xmlns:hb="http://www.w3.org/1998/Math/MathML" display="inline"> <hb:mrow> <hb:msup> <hb:mn>10</hb:mn> <hb:mn>5</hb:mn> </hb:msup> <hb:mtext> </hb:mtext> <hb:mtext> </hb:mtext> <hb:mi>Hz</hb:mi> </hb:mrow> </hb:math> .