Unicornをstartさせる時にエラーが出て困っております。

環境

AWS EC2
OS:Amazon Linux
Rails: 4.2.6
Ruby: 2.2.2
nginx: 1.8.1
unicorn: 5.1.0

エラー文

unicorn_rails -c /var/www/rails/rails_app/config/unicorn.conf.rb -D -E production

↑を叩くと、
↓が出る。

/home/ec2-user/.rbenv/versions/2.2.2/lib/ruby/gems/2.2.0/gems/unicorn-5.1.0/lib/unicorn/configurator.rb:88:in `block in reload': directory for pid=/var/www/rails/rails_app/tmp/pids/unicorn.pid not writable (ArgumentError)
       	from /home/ec2-user/.rbenv/versions/2.2.2/lib/ruby/gems/2.2.0/gems/unicorn-5.1.0/lib/unicorn/configurator.rb:84:in `each'
       	from /home/ec2-user/.rbenv/versions/2.2.2/lib/ruby/gems/2.2.0/gems/unicorn-5.1.0/lib/unicorn/configurator.rb:84:in `reload'
       	from /home/ec2-user/.rbenv/versions/2.2.2/lib/ruby/gems/2.2.0/gems/unicorn-5.1.0/lib/unicorn/configurator.rb:65:in `initialize'
       	from /home/ec2-user/.rbenv/versions/2.2.2/lib/ruby/gems/2.2.0/gems/unicorn-5.1.0/lib/unicorn/http_server.rb:76:in `new'
       	from /home/ec2-user/.rbenv/versions/2.2.2/lib/ruby/gems/2.2.0/gems/unicorn-5.1.0/lib/unicorn/http_server.rb:76:in `initialize'
       	from /home/ec2-user/.rbenv/versions/2.2.2/lib/ruby/gems/2.2.0/gems/unicorn-5.1.0/bin/unicorn_rails:209:in `new'
       	from /home/ec2-user/.rbenv/versions/2.2.2/lib/ruby/gems/2.2.0/gems/unicorn-5.1.0/bin/unicorn_rails:209:in `<top (required)>'
       	from /home/ec2-user/.rbenv/versions/2.2.2/bin/unicorn_rails:23:in `load'
       	from /home/ec2-user/.rbenv/versions/2.2.2/bin/unicorn_rails:23:in `<main>'
master failed to start, check stderr log for details

rails_app/tmp/pids/unicorn.pidをtouchで作ったりしましたがダメでした。

unicornの設定

unicorn.conf.rb
$worker  = 2
$timeout = 30
$app_dir = "/var/www/rails/rails_app" 
$listen  = '/var/www/rails/rails_app/tmp/sockets/.unicorn.sock'
$pid     = '/var/www/rails/rails_app/tmp/pids/unicorn.pid'
$std_log = '/vae/www/rails/rails_app/log/unicorn.log'
# set config
worker_processes  $worker
working_directory $app_dir
stderr_path $std_log
stdout_path $std_log
timeout $timeout
listen  $listen
pid $pid
# loading booster
preload_app true
# before starting processes
before_fork do |server, worker|
  defined?(ActiveRecord::Base) and ActiveRecord::Base.connection.disconnect!
  old_pid = "#{server.config[:pid]}.oldbin"
  if old_pid != server.pid
    begin
      Process.kill "QUIT", File.read(old_pid).to_i
    rescue Errno::ENOENT, Errno::ESRCH
    end
  end
end
# after finishing processes
after_fork do |server, worker|
  defined?(ActiveRecord::Base) and ActiveRecord::Base.establish_connection
end